fint reilu tice having the gwon centur ilal piioRt through t

fint reilu tice having the gwon centur ilal piioRt through thu giron point 4, 6

Solution

Given that the circle centre is at (0, 0) and it passes through the point (-4,6).

Circle equation is (x-h)² + (y-k)² = r²

Where (h,k) is center and r is radius.

Substitute (h,k) = (0, 0)

(x-h)² + (y-k)² = r²

(x-0)² + (y-0)² = r²

x² + y² = r²

Circle passes through (-4,6)

So, substitute (x, y) = (-4, 6) inx² + y² = r²

x² + y² = r²

(-4)² + 6² = r²

16 +36 = r²

r² =52

x² + y² = r²

x² + y² = 52

Therefore, x² + y² = 52 is the circle equation.

Option C is the correct option.