Question

The area of the circle whose centre is (1,2) and which passes through the point (4,6) is

• A. $25\pi$
• B. $100\pi$
• C. $92\pi$
• D. None of these

Answer 1

The correct option is A $25\pi$

Given,

Let $(h,k)$ be the centre of a circle with radius $r$.

Thus, its equation will be $(x-h{)}^2+(y-k{)}^2=r^2$

Given:

$h=1,k=2$

Equation of the circle $=(x-1{)}^2+(y-2{)}^2=r^2$ ...(1)

Also, equation (1) passes through $(4,6)$

$\therefore (4-1{)}^2+(6-2{)}^2=r^2$

$\Rightarrow 9+16=r^2$

$\Rightarrow r=5$

Area of circle,

$=\pi r^2$

$=\pi \times 25$

$=25\pi$