Question

Write an equation of a circle whose center is at the origin and contains the points (2,3)

Answer 1

The equation of circle of radius r and center (h,k) is given by

$(x-h)^2 + (y-k)^2 = r^2$

And it is given that the center is origin and it passes through (2,3).

So values of h and k are 0 each and values of x and y are 2 and respectively .

Substituting these values in the equation, we will get

$(2-0)^2 + (3-0)^2 = r^2 \\ 4+9 = r^2 \\ r^2 =13$

Substituting the values of h,k and r, we will get

$x^2 + y^2 = 13$