Question

Consider the two points F(−9, 0) and ????(9, 0) in the coordinate plane. What is the equation of the

ellipse given as the set of all points P in the coordinate plane satisfying FP + PG = 30? Write the
equation in the form
x^2 / a^2 + y^2 / b^2 = 1 with a and b real numbers, and explain how you obtain your
answer.

Answer 1

`(x^2)/(15^2) + (y^2)/(12^2) = 1`

Explanation:

Let's call P(x,y). For F(-9,0) and G(9,0), FP represents the distance between F and P, and PG, the distance between P and G. For an ellipse, F and G are the focus, which is in x ax (y = 0).

The equation is given by:

dFP + dPG = 2a

FP + PG = 30 --> 2a = 30 --> a = 15

The point in the x ax is called c = 9

And the relation between them are:

c² = a² - b²

9² = 15² - b²

b² = 225 - 81

b² = 144

b = √144

b = 12

So, the equation of the ellipse is:

`(x^2)/(15^2) + (y^2)/(12^2) = 1`