Question

Write the equation of the circle with center (0, 0) and (3, 6) a point on the circle. A) x2 + y2 = 9 B) x2 + y2 = 30 C) x2 + y2 = 45 D) x2 + y2 = 81

Answer 1

Answer:

The equation of a circle is x² + y² = 45 .

Option (C) is correct .

Step-by-step explanation:

The general form of the equation is

(x - h) ² +  (y - k)² = r ²

Where (h , k) are the centre of the circle and r is the radius .

As given

The circle with center (0, 0) and (3, 6) a point on the circle.

$r^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

$r^{2} = (3 - 0)^{2}+(6-0)^{2}$

$r^{2} =9+36$

$r^{2} =45$

As centre of the circle is (0,0) .

(x - 0) ² +  (y - 0)² = 45

x² + y² = 45

Therefore the equation of a circle is x² + y² = 45 .

Option (C) is correct .