Question

The number of circle having radius $5$ and passing through the point $(-2,0)$ and $(4,0)$ is ?

• A. $1$
• B. $2$
• C. $4$
• D. infinite

Answer 1

Answer: (B)

$2$

Here, radius of the circle is $5units.$

$\Rightarrow$ Diameter$=10units.$

The circle passes through the points $A(-2,0),B(4,0)$

$\therefore$ Distance between the points, $AB=\sqrt{{(4+2)}^2+{(0-0)}^2}=\sqrt{6^2}=6units$

LIne $AB$ is a chord for the circle of radius $5units$

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 circles passing through the points $(-2,0)$ and $(4,0)$.

The answer is $2$.