Which of the following sets of parametric equation equation

Which of the following sets of parametric equation (equation is attached )

Which of the following sets of parametric equations is equivalent to (x + 4)2 / 49 + (y + 5)2 / 36 = 1?

Solution

The easiest way to understand this is to do the following:

Let u = (x+4)/7 and v = (y+5)/6

Then, substituting into (x+4)²/49 + (y+5)²/36 = 1, we get

u² + v² = 1

This is the unit circle.

Thus, the obvious parametrization is (u,v) = (cos , sin )   

Then, as  u = (x+4)/7 ,cross-multiplying, x+4 = 7u, or x = 7u -4

As v = (y+5)/6, cross-multiplying, y + 5 = 6v, or y = 6v - 5

Thus, (x, y) = (7u - 4, 6v - 5) = ,substituting (u,v) = (cos , sin ),

(7 cos - 4, 6 sin - 5)

2 is the answer