A circle in the xy -plane has center ( 5,7)  and radius 2  Which of the following is an equation of the circle?

The correct answer is: <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>−</mo>
<mn>7</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo>=</mo>
<mn>4</mn>

Given: center of the circle: (5,7) ; radius = 2.
We know that the general equation of the circle is  where (h, k) is the center and r is the radius of the circle.
Let any point on the circle be x, y

This is the general equation of the given circle.
On further simplification, we get

Hence, option a is correct.