Question

Find the standard equation of the circle that passes through the point(1,5) and has the center(-2,1)

Answer 1

To find equation of the circle. Two things are required. The center of the circle and the radius of it.

Knowing the coordinates of the point that lies on the circle (1,5). you can calculate the radius if you calculate the distance from that point to the center of the circle.

Radius= sqrt( (1-(-2))^2 + (5-1)^2) = sqrt( 3^2 + 4^2 ) = sqrt( 25) = 5.

So you got the radius and the center point, you can put it in the general equation.

(y- a)^2 + (x-b)^2 = r^2

where a is the x coordinate of the center point and b is the y-coordinate, and r is the radius.

Fitting all the values in, you will get.

(y-1)^2 + (x+2)^2 =5^2