Question

Write the standard equation of a circle that passes through (-2, 10) with center (-2, 6)

Answer 1

Is it a graph??????????

Answer 2

By definition, the standard equation of the circle is given by:
 $(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2$
 Where,
 (xo, yo): coordinates of the center of the circle
 r: radius of the circle
 To find the radius of the circle, we use the formula of distance between points.
 We have then:
 $r=\sqrt{(x2-x1)^2+(y2-y1)^2}$
 Substituting values:
 $r=\sqrt{(-2-(-2))^2+(6-10)^2}$
 $r=\sqrt{(-2+2)^2+(-4)^2}$
 $r=\sqrt{(0)^2+16}$
 $r=\sqrt{(0+16}$
 $r=\sqrt{(16}$
 $r=4$
 Then, the center of the circle is:
 $(xo, yo) = (-2, 6)$
 Substituting values in the general equation we have:
 $(x-(-2))^2+(y-6)^2=4^2$
 Rewriting:
 $(x+2)^2+(y-6)^2=16$
 Answer:
 The standard equation of the circle is:
 $(x+2)^2+(y-6)^2=16$