Conics Definition and 59 Threads

I need to find the equation of a parabola in standard form if the domain of an arch under a bridge is {-50 <= x <= 50} and the range is {0<=y<=20} The span of the arch is 100 metres and the height is 20 metres. standard form of a parabola is (x-h)^2=4p(y-k) i know the vertex is...

I think that I'm over looking something with this problem. Below is the equation of an hyperbola in polar form. R=\frac{1}{1 + 2cos{\theta}} when \theta =\pi shouldn't R = -1? And not R= 1 Am I over looking some property of the \cos function? Even when i evalute this expression at...

Your task is to design a curved arch similar to the a tunnel for cars. with a horizontal span of 100 m and a maximum height of 20 m. Using a domain of {x:-50<=x<=50} and {y:0<=y<=20} determine the following types of equations that could be used to model the curved arch. the equation of a...

I have been taught that the equation Ax^2 + Cy^2 +Dx + Ey +F = 0 represents a general form of conics. Then the conditions of the coefficients in the equation could identify which type of conics the equation represents... Circle: A=C Ellipse: A does not=C and AC>0 Hyperbola: AC<0 and...

6x^2 + 2y^2 - 9x +14y -68=0 a) which conic is represented by the equation why? I think the ellipse is represented by the equation because a does not = b and ab >0 b)What value of "a" would transform the conic into a circle? I think when a=b and ab>0 then the conic will be...

A flash light is pointed at a wall so that the angle between the beam and the wall is 65 degrees a) which conic section is produced? I am not sure if this is asking for the shape but I think the answer is an ellipse b) How would you adjuct the angle of the beam to produce a circle on the...

Problem I: (The coeffiecients throw me off, I don't know what I'm supposed to do with them) 9x^2 + 16y^2 = 144 Determine: a) coodinates of the centre b) lengths of the major and minor axes Problem II: Sketch a graph of the ellipse 4x^2 + (y+1)^2 = 9 PS: For...

Ok I seem to be having problems with changing the general form of a conic to standard form. I'm mainly confused with how to factor, since I haven't done it in a while, as well as how to go about completing the square. Here's one of my problems: 2x^2 + y^2 + 12x – 2y + 15=0 I rearranged...

"A line segment through a focus with endpoints on the ellipse and perpendicular to the major axis is a latus rectum of the ellipse. Therefore, an ellipse has two latus recta. Show that the length of each latus rectum is 2b^2/a." I've been stuck on this for a little while now. Can anyone point...