Radius & Center of Circle: Solving for x^2+4x+y^2-3y=0 | Final Review Question"

  • Thread starter Thread starter imdapolak
  • Start date Start date
  • Tags Tags
    Circle Radius
AI Thread Summary
To find the radius and center of the circle represented by the equation x^2 + 4x + y^2 - 3y = 0, one must complete the square for both the x and y terms. Completing the square for x yields (x + 2)^2 - 4, and for y yields (y - 1.5)^2 - 2.5. This reformulates the equation into the standard circle form (x - a)^2 + (y - b)^2 = r^2. The center of the circle is located at (-2, 1.5) and the radius is √2. Understanding how to manipulate the equation into this form is crucial for identifying the circle's properties.
imdapolak
Messages
10
Reaction score
0
1. What are the radius and center of this circle? x^2+4x+y^2-3y=0



Homework Equations





3. Another question on my final review I don't recall exactly how to set up or what steps I need to do in order to solve this problem. Any help is appreciated
 
Physics news on Phys.org
If I gave you the equation in the form (x-a)^2+(y-b)^2=r^2, could you tell me the location of the center of the circle and its radius?

If so, just complete the square for both x and y in your above equation in order to get it into this form.
 
The equation of a circle is of the form (x-a)^2+(y-b)^2=r^2. So you want to write x^2+4x as (x-a)^2+constant. In other words complete the square.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Circle equation coefficient conditions
Replies
3
Views
2K
How do you solve in terms of y 4x^2-2xy+3y^2=2
Replies
5
Views
2K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
Replies
10
Views
2K
A non-intersecting family of circles
Replies
3
Views
2K
Equation of Circle Passing Through Given Point and Line with Given Radius
Replies
6
Views
2K
Equation of a circle from given conditions
Replies
11
Views
2K
Find the center of a circle given a tangent line & point
Replies
2
Views
3K
Mapping Circle to Ellipse with Dilation?
Replies
2
Views
3K
Solve for unknown radius without trig
Replies
21
Views
4K
Solving a Circle Problem: Finding Radius and Center | Math Forum Help
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top