Need help with math

Question

How do I write the standard form of an equation of a circle if

Center: (-1,2); solution point: (3,4)

Answer 1

The General Equation for a Circle is ( x - h )² + ( y - k )² = r² where ( h, k ) is the center and r = radius. 

We are given the center (-1,2) so we can rewrite our equation as ( x + 1 )² + ( y - 2 )² = r²

To find the radius, we need to find the distance between the center (-1,2) and a point on the circle (3,4). To do this we should us the distance formula to find the radius.

Distance formula is distance=√( ( x₂ - x₁ )²+( y₂ - y₁ )²)

Plug in the points: √( ( 3 + 1 )²+( 4 - 2 )²)

Simplify the expression: √( ( 4 )²+( 2 )²) = √( 16 + 4) = √20

Since the radius equals the distance between the center (-1,2) and a point on the circle (3,4), radius is √20

Plugging this back into our general equation for a circle, we get: ( x + 1 )² + ( y - 2 )² = 20