Write the standard form of the equation of the circle with the center at (0,2) that passes through the point (7,3) .
A) $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 50$
B) $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 58$
C) $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$
D) $( x - 2 ) ^ { 2 } + y ^ { 2 } = 58$
E) $( x + 2 ) ^ { 2 } + y ^ { 2 } = 50$

Question

Quizplus · Accepted Answer

The standard form of the equation of a circle with center $(h,k)$ and radius $r$ is:
$$(x-h)^2+(y-k)^2=r^2$$
In this case, the center is $(0,2)$, so $h=0$ and $k=2$. We need to find the radius, which is the distance between the center $(0,2)$ and the point $(7,3)$:
$$r=\sqrt{(7-0)^2+(3-2)^2}=\sqrt{50}$$
So, the equation of the circle is:
$$(x-0)^2+(y-2)^2=50$$
Simplifying, we get:
$$x^2+(y-2)^2=50$$
which matches choice C.

Write the Standard Form of the Equation of the Circle x2+(y+2)2=50x ^ { 2 } + ( y + 2 ) ^ { 2 } = 50x2+(y+2)2=50

Write the Standard Form of the Equation of the Circle $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 50$