Question

Write the equation of a circle with center (-2,4) and passes through the point (-6, 7)

Answer 1

The equation for a circle is: (x - h)² + (y - k)² = r²
h represents the x-coordinate of the center,
k represents the y-coordinate of the center,
r represents the radius of the circle.

The center is given as (-2, 4) so plug in -2 for h and 4 for k.

Now we need to find the radius. 
The distance from the center to any point on the circle is the radius. 
Use the distance formula to find the distance between (-2,4) and (-6, 7).
d = $\sqrt{ (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
d² = $( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2}$
   = (-2 + 6)² + (4 - 7)²
   = (4)² + (-3)²
   =  16  +  9
   =  25
Plug is 25 for r²

Answer: (x + 2)² + (y - 4)² = 25