Question

Suppose a circle with center (14, 9) passes through point (16, 12). Which equation represents the circle?

Answer 1

Answer:

The equation that represents the circle is $(x-14)^{2}$ + $(y-9)^{2}$ = 13

Step-by-step explanation:

Given the center of circle (14,9) passes through point (16,12)

We know that the equation of circle is

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

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

From given data (x,y) is (16,12) and (h,k) is (14,9). Substituting these values in equation of circle, we get

$(16-14)^{2}$ + $(12-9)^{2}$ = $r^{2}$

$r^{2}$ = $2^{2}$ + $3^{2}$

$r^{2}$ = 13

Substituting the values of (h,K) and  $r^{2}$ as (14,9) and 13 respectively in equation of circle, we get

$(x-14)^{2}$ + $(y-9)^{2}$ = 13

Hence the equation that represents the circle is $(x-14)^{2}$ + $(y-9)^{2}$ = 13