Consider the two points f(−9, 0) and , 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.

Step-by-step 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: