Question

The number of a circle having a radius of $5$ and passing through the points $\left(-2,0\right)$ and $\left(4,0\right)$ is

• A. One
• B. Two
• C. Four
• D. Infinite

Answer 1

The correct option is B

Two

Explanation for correct option

Given, radius of the circle is $5\mathrm{unit}$

Therefore diameter is $10\mathrm{unit}$

The circle passes through the point $A$$\left(-2,0\right)$ and $B$$\left(4,0\right)$

Therefore distance between the point $AB=\sqrt{{\left(4+2\right)}^2+{\left(0-0\right)}^2}=\sqrt{36}=6\mathrm{units}$

Line $AB$ is a chord for the circle of radius $5\mathrm{unit}$

There are two cases

1. The centre of the circle will be below the chord $AB$
2. The centre of the circle will be above the chord $AB$

Hence there will be two circle passing through the point $\left(-2,0\right)$ and $\left(4,0\right)$

Hence, the correct option is $\left(\mathrm{B}\right)$