Question

Using a directrix of y = -3 and a focus of (2, 1), what quadratic function is created?

Answer 1

Find what relation you have between x and y so that
\[
(x-2)^2+(y-1)^2=(y+3)^2
\]

Answer 2

Can you finish it now?

Answer 3

Square both sides and simplify to get
\[
-4 - 4 x + x^2 - 8 y =0
\]
Solve for y in terms of x

Answer 4

You see the \( y^2\) cancels

Answer 5

Solving gives
\[
y=\frac{1}{8} \left(x^2-4
x-4\right)=\frac{x^2}{8}-\frac{x}{2}-\frac{1}{2}
\]
What is the quadratic?

Answer 6

f(x)=1/8(x-2)^2-1?

Answer 7

@eliassaab

Answer 8

Yep, thanks

Answer 9

YW