Question

The area of a circle whose centre is $\left( {h,k} \right)$ and radius $a$ is
A. $\pi \left( {{h^2} + {k^2} - {a^2}} \right)$
B. $\pi \left( {{a^2}hk} \right)$
C. $\pi \left( {{a^2}} \right)$
D. None of these

Answer 1

Hint: In this question we are given the coordinates of the centre of the circle $\left( {h,k} \right)$. Also, the radius of the circle is given i.e., $a$. Here, we need to find the area of the circle. Use the formula area of the circle $ = \pi {r^2}$ and put the value of radius.

Formula used:
Area of circle $ = \pi {r^2}$, where $r$ is the radius of a circle

Complete step by step solution:
A circle is a closed curve drawn from a fixed point known as the centre, with all points on the curve being the same distance from the centre point. When dealing with such problems, keep in mind that the only parameter we need in a circle is its radius to calculate the area, circumference, and so on of any part of it. This approach will solve your problem.
Given that,
Centre of the circle is at $\left( {h,k} \right)$
Radius of the circle is $a$
Using formula,
Area of circle $ = \pi {r^2}$
$ = \pi {a^2}$

Hence, Option (C) is the correct answer i.e., $\pi \left( {{a^2}} \right)$

Note: For calculating the amount of space occupied by a circular field or plot, use the area of the circle formula. If you have already got a plot that needs fencing, using the formula of circumference will allow you to determine how much fencing is needed. Or, if you would like to purchase a tablecloth, what proportion cloth would be required to entirely cover it? In order to solve such problems, the concepts of area and perimeter are introduced in mathematics. But the question that "does a circle have volume?" is one that most people frequently ask. The response is "No." A circle has no volume because it is a two-dimensional object. It has a perimeter and an area.