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

C)

`{x}^(2) + {y}^(2) = 10`

Step-by-step 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) } = √(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)= {( √(10)) }^(2)`

`{x}^(2) + {y}^(2) = 10`