SOLUTION: Find an equation for the circle C with center at (3, -5) tangent to the y-axis. Find an equation for the parabola B with focus (3, 1) and directrix x = 7.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find an equation for the circle C with center at (3, -5) tangent to the y-axis. Find an equation for the parabola B with focus (3, 1) and directrix x = 7.      Log On


   

Question 314495: Find an equation for the circle C with center at (3, -5) tangent to the y-axis.
Find an equation for the parabola B with focus (3, 1) and directrix x = 7.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a circle centered at (h,k) with a radius R is:
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
Tangent to the y-axis means that the x-distance from the center to y-axis is equal to R.
R=3
(h,k)=(3,-5)
%28x-3%29%5E2%2B%28y%2B5%29%5E2=3%5E2
%28x-3%29%5E2%2B%28y%2B5%29%5E2=9

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The focus is located at (3,1).
The directrix is x=7.
The distance from the vertex to focus is equal to the distance from vertex to directrix.
The vertex is located at (5,1).
The general equation for a horizontal parabola is,
-4p%28x-h%29=%28y-k%29%5E2
p is the distance from the focus to vertex.
p=2
(h,k) is the vertex.
{h,k)=(5,1)
-4p%28x-h%29=%28y-k%29%5E2
4%282%29%28x-5%29=%28y-1%29%5E2
-8%28x-5%29=%28y-1%29%5E2
x=-%281%2F8%29%28y-1%29%5E2%2B5