Find all points with coordinates of the form (a, a) that are a distance 7 from P(−5, 2).

Answer 1

We get equation: (a + 5)² + (a - 2)² = 7²,

a² + 10a + 25 + a² - 4a + 4 = 49, 2a² + 6a - 20 = 0, a² + 3a - 10 = 0, (a + 5)(a - 2) = 0;

a+ 5 = 0 or a - 2 = 0, a = - 5 or a = 2.

Points (- 5, - 5) and (2,2) distant by 7 from point (- 5, 2)