Maths-

General

Easy

Question

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

- <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>

<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>

Hint:

### The equation of a circle with center(h, k) and radius r will be

## 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.

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