find the points

Question

Find all points having an​ x-coordinate of 6 whose distance from the point ​(3​,−8​) is 5.

Answer 1

The points must be on the circle:

(x - 3)² + (y + 8)² = 25

For x = 6

3² + (y + 8)² = 25

(y + 8)² = 16

y + 8 = ±4

y = -12 or y = -4

The points are (6, -4) and (6, -12