Circle Definition and 1000 Threads

A circle whose center is (2, 1) intercepts a line whose equation is 3x + 4y + 5 = 0 at point A and B. If the length of AB = 8, then the equation of the circle is ... A. $$x^2+y^2-24x-2y-20=0$$ B. $$x^2+y^2-24x-2y-4=0$$ C. $$x^2+y^2-12x-2y-11=0$$ D. $$x^2+y^2-4x-2y+1=0$$ E. $$x^2+y^2-4x-2y+4=0$$...

Determine the graph of $x^2+y^2+6x+8y+9=0$ $\begin{array}{rll} \textsf{rewrite} &(x^2+6x )+(y^2+8y)=-9\\ \textsf{complete square} &(x^2+6x+9)+(y^2+8y+16)=-9+9+16\\ \textsf{simplify equation} &(x+3)^2+(y+4)^2=16=4^2\\ \textsf{observation} &C(-3,-4), \quad R=4...

Chapter 1, Section 1.2 Write the standard form of the equation of the circle with the given characteristics. 72. Center: (−2, −6); Solution point: (1, −10) Solution: given: Center: (−2, −6); => h=-2, k=-6 => then (x - (-2))^2 + (y - (-6))^2 = r^2 (x +2)^2 + (y +6)^2 = r^2... I then use...

Chapter 1, Section 1.2 Write the standard form of the equation of the circle with the given characteristics. 74. Endpoints of a diameter: (11, −5), (3, 15) I want to know if the following steps are correct for me to answer the above question. Steps: 1. Find the distance between the points...

Hello! I have an application where I need to find the center of a circle where I am having trouble coming up with a simple way to do this. The diameter of the circle is known and i want to be able to determine the location of it where only a portion of the circle is known. (see the image...

Rectangle ABCD is inscribed in the circle shown. If the length of side $\overline{AB}$ is 5 and the length of side $\overline{BC}$ is 12 what is the area of the shaded region? $a.\ 40.8\quad b.\ 53.1\quad c\ 72.7\quad d \ 78.5\quad e\ 81.7$ well to start with the common triangle of 12 5...

So as the summary suggests, I am studying Electromagnetism, magnetic properties of matter and Magnetization vector in particular. As a first example and to introduce the Magnetization vector (M), my textbook shows a ferromagnetic substance in a uniform magnetic field (B). Then, every atom of...

Hi, I was working through a filter design problem and got stuck on a concept. Scenario: Let us say we have the following pulse transfer function and the sampling frequency is ## f_s = 50 \text{Hz} ##. G(z) = \frac{1}{3} \left( 1 + z^{-1} + z^{-2} \right) The zeros of the transfer function...

Here's what I did: ∮ B * dl ＝μ0 ＊ I ∮ AR * 2π*R ＝μ0 ＊ I ∮ 2π*AR^2 / μ0 = I ∮ 2π*AR^3 / 3μ0 = I Where did I do wrong?

how to circle a equation in a straight line y= 2x-1 y = x^2+ 2 x –y = 1 x = y + 5 y = – x^2 + 5 pls help me

A, B and C are points on a circle with center O. Angle ABC = $75°$ . The area of the shaded segment is $200cm^2$ . Calculate the radius of the circle. Answer correct to $3$ significant figures.

Hey! :giggle: Make a drawing for each of the values of the angle below indicating the angle at the unit circle (in other words: $\text{exp} (i \phi )$) and its sine, show cosine, tangent and cotangent. Give these four values explicitly in every case (you are allowed to use elementary...

Given: x^2+xy+y^2=18 x^2+y^2=12 Attempt: (x^2+y^2)+xy=18 12+xy=18 xy=6 y^2=12-x^2 (12)+xy=18 xy=6 Attempt 2: xy=6 x=y/6 y^2/36+(y/6)y+y^2=18 43/36y^2=18 y ≠ root(6) <- should be the answer Edit: Just realized you can't plug the modified equation back into its original self I plugged y=6/x...

My Effort: Circumference = pi•d 10 •pi = pi•d 10•pi/pi = d 10 = d, where d is the diameter of the circle. Area = pi•r^2, where r is the radius of the circle. Diameter = 2 times the radius. 10pi = 2r 10pi/2 = r 5pi = r A = pi•r^2 A = pi(5pi)^2 A = 25•pi^3, which makes no sense. Only...

Hi, I take a big number of disks to composed a circle of a radius of 1 m, the blue curved line is in fact several very small disks: I take a big number of disks to simplify the calculations, and I take the size of the disks very small in comparison of the radius of the circle. The center A1 of...

A concentric cirlce has two circles with the same center, but a different radii. We are given a pie with radius ##r##. A circular cut is made at radius ##r## such that the area of the inner circle is ##1/2## the area of the pie. We know that the formula to calculating the area of a circle is...

Why is it that the radius of the unit circle is 1?

1. Using the formula for the arc length; s= θr I have endeavoured to find the angle AOB sine both the arc length and radius are known; 11= θ*8 θ=11/8=1.375 rad I actually do not think that this can be correct as it seem to simplistic a response. Have I misinterpreted the question or used the...

This is a problem in two dimensions. Consider an obstacle (in the form of a line segment) placed at ##x=1##, ##0 \leq y \leq 1##. Now consider the circle of radius ##1## and center at ##(x_0,1)## [initially at time ##t=0##] moving towards right with a combination of: (i) Angular speed of ##2...

From a freebody analysis I got, $$ \vec{r} \times \vec{F} = |r| |F| \sin( 90 - \theta) = (R-r) mg \cos \theta$$ and, this is equal to $$ I \alpha_1$$ where the alpha_1 is the angular acceleration of center of mass of small circle around big one, $$ I \alpha = (R-r) mg \cos \theta$$ Now...

What you think about this system:? F*cosw - k(x1+x2) - k(x1-x2) = mx1'' -k(x1+x2) - k(x1-x2) = mx2''

We have a circle (x^2 + y^2=2) and a parabola (x^2=y). We put x^2 = y in the circle equation and we get y^+y-2=0. We get two values of y as y=1 and y=-2. Y=1 gives us two intersection point i.e (1,1) and (-1,1). But y=-2 neither it lie on the circle nor on the parabola. The discriminant of the...

My textbook says "A is the area of the circle enclosed by the current" (produced by an electron in a hydrogen atom), A = ##\pi r^2 \sin(\theta)^2##. I don't understand where the ##\sin(\theta)^2## comes from.

Five identical semicircles are arranged as shown. Find the diameter of one circle. \draw (0,0) -- (16.5, 0); \begin{scope} \clip (0,0) rectangle (4.5,4.5); \draw (2.25,0) circle(2.25); \draw (0,0) -- (4.5,0); \end{scope} \begin{scope} \clip (6,0) rectangle (10.5,4.5); \draw...

Summary:: For finding the electric field at P in the photo below, may I select a gaussian surface circular? [Mentor Note -- thread moved to the schoolwork forums, so no Homework Template is shown]

How do I algebraically prove how many times the line y=-5 intersects the circle (x-3)^2 + (y+2)^2 =25?

I don't get how ball moves in a vertical circle,we say tension provides centripetal force to the ball, i have posted a image in this post and in I which I have shown that their is a downward force mg and upward velocity,in this what will cause tension in the rope...from non inertial frame it is...

In this case, I know there won't be any net efield in the x direction because it cancels out with each other. The problem is dealing with the y axis. Am I supposed to presume an angle for each of them or what should I do instead? Thanks

So this "seemingly simple" geometry and idea caught my attention. See the video in the link from 9:00 minute They talk about a specially designed nuclear fuel canister/bundle, now there is this geometry where they have a cylinder with smaller diameter and then a cylinder with a larger...

So, true story: I made a large circular tortilla. Ate half of it. Then decided to put the rest into the fridge on a smaller plate.I raised the knife to cut the remaining semi-circle in two, and then went : "Hmmmmmmmm...". Anyway, it's in the fridge now with an approximate solution, but I'm...

The center of circle L is located in the first quadrant and lays on the line y = 2x. If the circle L touches the Y-axis at (0,6), the equation of circle L is ... a. $$x^2+y^2-3x-6y=0$$ b. $$x^2+y^2-12x-6y=0$$ c. $$x^2+y^2+6x+12y-108=0$$ d. $$x^2+y^2+12x+6y-72=0$$ e. $$x^2+y^2-6x-12y+36=0$$...

The circle $$x^2+y^2+px+8y+9=0$$ touches the X-axis at one point. The center of that circle is ... a. (3, -4) b. (6, -4) c. (6, -8) d. (-6, -4) e. (-6, -8) I already eliminated option c and e since based on the coefficient of y in the equation, the ordinate of the center must be -4. However, I...

Hi everyone, I am confused in this question. First I solved it by noticing that the gradient of the function will be zero (without substitution the hit) I got that it's a conservative field so the integral should be zero since it's closed path. Then I solved it by the hit and convert it as any...

The function f is defined by $$f(x)=\sqrt{25-x^2},\quad -5\le x \le 5$$ (a) Find $f'(x)$ apply chain rule $$ \dfrac{d}{dx}(25-x^2)^{1/2} =\dfrac{1}{2}(25-x^2)^{-1/2}2x =-\frac{x}{\sqrt{25-x^2}}$$ (b) Write an equation for the tangent line to the graph of f at $x=-3$...

Hello everyone! I have been looking for a general equation for any regular polygon and I have arrived at this equation: $$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$ Where x is the side length and n the number of sides. So I thought to myself "if the number of sides is increased as to almost look...

33.33 RPM (1min/60second)(6.28 radian/1 revolution) = 3.45 rad/s linear velocity=3.45 rad/s * 0.1524m=0.526 m/s linear acceleration= (0.526 m/s)^2 /(0.1524m)=1.814 m/s^2 1.814 m/s^2=(0.1524m)(rotational acceleration) rotational acceleration=11.9 rad/s^2 ω1= (3.45 rad/s)+(11.9rad/s^2)(10s)...

Hello: I am looking for a formula that can help me determine the collapse and deformation strengths of plastic tubing. I have been scouring the internet for this information and i have yet to find a satsifactory formula. I have found a formula that seems pretty wide spread ~ however it gives me...

A figure is made from a semi circle and square. With the following dimensions, width = w, and length = l. Find the maximum area when the combined perimiter is 8 meter. I first try to construct the a function for the perimeter. 2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7 Next I insert this...

if it helps, the answer is supposed to be my colleagues and I can't figure out how to come to that answer. It's probably something simple. edit: I tried to solve it by inscribing an octagon, and then finding the distance from the center of the octagon to the side of the octagon. but I got 1 +...

find standard eqations of circles that have centers on 4x+3y=8 and are tangent to both the line x+y=-2 and 7x-y=-6 What I got is $$4a=–4\pm3r\sqrt2$$ and $$b=4\pm r\sqrt2$$. Dunno how to continue from here.

Hi! My main problem is that I don't understand what the problem is telling me. What does it mean that the surface is a flast disc bounded by the circle? Is the Gauss surface the disc? Does that mean that inside the circle in the figure, there is a disc? Can you give me some guidance on how to...

Well, I tried decomposing velocity into its components on the radial and angular axis. But I have problems with the angles because in some parts of the trajectory the velocity is on the angular coordinate, but in other parts it isn't. I mean, I can't say ##V=V e_\theta## because it's not always...

Homework Statement: How or why does inertia caused the water in a bucket not to fall out when spinning in a vertical circle. Homework Equations: Is the bucket catching the water? I know Inertia is the resistance of any physical object to any change in its velocity.

F = mac = (mv2 / r)

So I figured out the potential is: dV = (1/(4*Pi*Epsilon_0))*[λ dl/sqrt(z^2+a^2)] . From that expression: We can figure out that since its half a ring we have to integrate from 0 to pi*a, so we would get: V = (1/(4*Pi*Epsilon_0))*[λ {pi*a]/sqrt(z^2+a^2)] In that expression: a = sqrt(x^2+y^2)...

I was just reading an intro text about GR, which considers the circumference of a circle on a sphere of radius R as an example of intrinsic curvature - the thought being that you know you're on a 2D curved surface because the circle's circumference will be less than ##2\pi r##. They draw a...

Hi. I have been trying to calculate the real definite integral with limits 2π and 0 of ## 1/(k+sin2θ) ## To avoid the denominator becoming zero I know this means |k|> 1 Making the substitution ##z= e^{iθ}## eventually ends up giving me a quadratic equation in ##z^2## with 2 pairs of roots...

find an equation of the circle passing through the given points 85 Given $(-1,3),\quad (6,2),\quad (-2,-4)$ since the radius is the same for all points set all cirlce eq equal to each other $(x_1-h)^2+(y_1-k)^2=(x_2-h)^2+(y_2-k)^2=(x_3-h)^2+(y_3-k)^2$ plug in values...

Dear all, Attached is a picture of a circle. The lower tangent line is y=0.5x. The center of the circle is M(4,7) while the point A is (3,6). I found the equation of the circle, it is: $(x-4)^{2}+(y-7)^{2}=20$ and I wish to find the dotted tangent line. I know that it is parallel to the...