Question

Derive the equation of a parabola with a focus of (-7,5) and a directrix of y=-11

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Answer 1

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EQUATION : (y + 11)^2/120 = (x + 7)^2 + (y-5)^2

Explanation:

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Answer 2

The equation of the parabola is;

(y + 11)^2/120 = (x + 7)^2 + (y-5)^2

Explanation:

Here, we are given the focus (-7,5) and the directix y = -11

We proceed to find the equation of the parabola

That would be in the form;

(y- mx - b)^2 /m^2 + 1 = (x- h)^2 + (y-k)^2

Let’s write the directix in the form y = mx + b

This shows that m = 0 and b = -11

Also h = -7 and k = 5

So let’s substitute;

(y + 11)^2 /(-11^2 + 1) = (x+7)^2 + (y-5)^2

= (y + 11)^2/120 = (x + 7)^2 + (y-5)^2