Question

The number of feet of normals from the point $\left(7,-4\right)$ to the circle $x^2+y^2=5$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B

$2$

Explanation for the correct option:

Find the number of intersects when the normal is drawn from the given point.

An equation of circle $x^2+y^2=5$ and a point $\left(7,-4\right)$ is given.

Find the location of the given point with respect to the given circle.

Rewrite the given equation as $x^2+y^2-5=0$.

Substitute $x=7$ and $y=-4$ in the equation of the circle.

$$\begin{gathered} {\left(7\right)}^2+{\left(-4\right)}^2-5=49+16-5 \\ \Rightarrow {\left(7\right)}^2+{\left(-4\right)}^2-5=>0 \end{gathered}$$

Which implies that the given point is outside the given circle.

Therefore, the number of intersections when a normal is drawn from the given point to the given circle is $2$.

Hence, option $B$ is the correct option.