Question

Write the equation of the circle with center (0, 0) and (−1, −3) a point on the circle. A) x2 + y2 = 4 B) x2 + y2 = 5 C) x2 + y2 = 10 D) x2 + y2 = 16

Answer 1

ANSWER

C)

${x}^{2} + {y}^{2} = 10$

EXPLANATION

The center of the circle is (0,0).

The circle passes through (-1,-3).

The radius can be obtained using the distance formula:

$r = \sqrt{(0 - 1)^{2} + {(0 - - 3)}^{2} } = \sqrt{10}$

The equation is given as:

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

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

This implies that;

$( {x - 0)}^{2} + ( {y - 0)}^{2}= {( \sqrt{10)} }^{2}$

${x}^{2} + {y}^{2} = 10$

Answer 2

Answer: C

Step-by-step explanation: