Question

A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is units. The point (-15, ) lies on this circle. NextReset

Answer 1

hello :
an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a = -7 and b = -1 (Center at: A(-7,-1) )
r = AP.... P(8,7)
r² = (AP)²
r² = (8+7)² +(7+1)² =225+64=289 ...... so : r = 17
an equation of the circle that satisfies the stated conditions.
Center at A(-7,-1), passing through P(8, 7) is :

(x+7)² +(y+1)² = 289

The point (-15,y ) lies on this circle : (-15+7)² +(y+1)² = 289....(subsct : x= -15)
(y+1)² = 225
(y+1)² = 15²
y+1 = 15 or y+1 = -15
y = 14 or y = -16
you have two points : (-15,14) , (-15, -16)