Question

Write the standard form of the equation of the circle with the given characteristics.
Center: (3, −1); solution point: (−1, 2)

Answer 1

First find the distance from the center to the point. That will be the radius.

Answer 2

eqn of a circle: \[\left( x-a ^{2} \right)+\left( y-b \right)^{2}=r ^{2}\]
where (a,b) is the centre point and r is the radius

now u just need radius. Solution point (-1,2) lies on the circumference of the circle. Thus finding the distance btw this solution point and the center would give u your radius.



Since, a^2 + b^2 = c^2

3^2+ 4^2 = c^2
c= 5

Thus eqn is:\[\left( x-3 \right)^{2}+\left( y+1 \right)^{2}=5^{2}\]