What is the standard form of the equation of the parabola with a directrix at x=23 and a focus at (5,5)?

1 Answer
Harish Chandra Rajpoot
Jun 19, 2018

The equation of parabola will be: (y-5)^2=-36(x-14)

Explanation:

Given equation of directrix of parabola is x=23 & the focus at (5, 5). It is clear that it is a horizontal parabola with sides diverging in -ve x-direction. Let general equation of parabola be
(y-y_1)^2=-4a(x-x_1) having equation of directrix: x=x_1+a & the focus at (x_1-a, y_1)
Now, comparing with given data, we have x_1+a=23, x_1-a=5, y_1=5 which gives us x_1=14, a=9 hence the equation of parabola will
(y-5)^2=-4\cdot 9(x-14)
(y-5)^2=-36(x-14)

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