Question

The shortest distance of the point $(6,–8)$from the circle $x^2+y^2=36$, is

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is A

$4$

Explanation for the correct option.

Find the shortest distance of the point from the circle.

Given,

The equation of the circle is $x^2+y^2=36$.

The coordinate of the point is $(6,–8)$.

Center of the circle $=(0,0)$

The radius of the circle $=\sqrt{36}=6units$

Now, the distance of the center from the point

$$\begin{gathered} =\sqrt{{(6-0)}^2+{(-8-0)}^2} \\ =\sqrt{36+64}=\sqrt{100} \\ =10units \end{gathered}$$ [Applying Distance formula]

So, the shortest distance of the point $(6,–8)$from the circle

$=10-6=4units$

Hence, option $A$ is the correct answer.