A parabola can be drawn given a focus of (8, 6) and a directrix of x=4 Write the equation of the parabola in any form. Answer:

Question

asked May 15, 2022 65.2k views

1 Answer

Posthumecaver · Answer 1 · 2022-05-20T16:15:12+0000

Answer:

The equation of the parabola in vertex form is
$x-6 = (1)/(16)\cdot (y-6)^(2)$ .

Explanation:

Since the directrix is of the
x = a , then the equation of the parabola in vertex form is of the form:

$x-h = (1)/(4\cdot p)\cdot (y-k)^(2)$ (1)

Where:

- Dependent variable.

- Independent variable.

- Least distance between focus and directrix.

,
- Coordinate of the vertex.

The least distance between focus and directrix is determined by Pythagorean Theorem:

$p = \sqrt{(8-4)^(2)+(6-6)^(2)}$

p = 4

Now, we determine the location of the vertex by the following vectorial formula:

$(h,k) = F(x,y) - (0.5\cdot p, 0)$ (2)

If we know that
p = 4 and
F(x,y) = (8,6) , then the location of the vertex is:

(h,k) = (8,6) -(2, 0)

(h,k) = (6,6)

And the equation of the parabola in vertex form is
$x-6 = (1)/(16)\cdot (y-6)^(2)$ .