Question

Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1.

Answer 1

Deriving equation of the parabola with focus and directrix requires you to use the combined distance formula
\[\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(y_2-y_1)^2}\]

Plug in the focus on the left side of the equation and plug in the directrix on the right side.

Answer 2

would it be 1/2(x-6)^2+3/2 ?

Answer 3

@izuru

Answer 4

Okay so first you substitute your information into the equation. What you do next is to remove the radicals. After you've removed the radicals, distribute the y-term binomials. Simplify and then isolate the x terms. Lastly, isolate the y term to get the equation.

Answer 5

And yes that's the correct answer, sorry just explaining the process

Answer 6

okay thank you!

Answer 7

You're welcome!