Analytic geometry

Question

A circle with center at (0,0) passes through the point (-12,5)

a) determine the radius of this circle

b)state the equation of this circle

Answer 1

The standard equation of a circle is:

(x-h)² + (y-k)² = r²

where (h,k) is the circle's center and r is its radius. We are given that the center is at (0,0), so h = k = 0 and the equation is:

(x-h)² + (y-k)² = r²

(x-0)² + (y-0)² = r²

x² + y² = r² (This is the answer to part b)

To find the radius, plug in the given point (-12,5):

x² + y² = r²

(-12)² + 5² = r²

144 + 25 = r²

Can you finish it? You can also find the radius by using the distance formula between the center at (0,0) and the given point (-12,5).