Consider a horizontal stretch by a factor of 1/2. Then each point (x, y) on the plot becomes (x/2, y). Let's call this new point (x', y'); then x' = x/2 and y' = y, or x = 2x' and y = y'. Substituting x(x') and y(y') into the original equation, we get (2x')^2 + (y')^2 = 1, which is the new equation. The remaining steps can be done similarly.

This is not an equation. However, for any R, (x-2)^2 + (y+3)^2 = R^2 is a circle with center (2, -3) and radius R.

Since a terminal arm is in the third quadrant, sin Ɵ and cos Ɵ are negative. Denoting x = -cos Ɵ and y = -sin Ɵ, you can write a relation between x and y and then use the Pythagorean theorem to find x and y.