The area of the circle centred at (1,2) and passing through (4,6) is

Options

A. `5pi` sq unit
B. `5pi` sq unit
C. `5pi` sq unit
D. None of the above

Answer

D

Explanation

The equation of a circle centred at (1,2) and passing through (4,6) is
`(x-1)^(2)+(y-2)^(2)=(4-1)^(2)+(6-2)^(2)`
`Rightarrow x^(2)+y^(2)-2x-4y+1+4=9+16`
`Rightarrow x^(2)+y^(2)-2x-4y-20=0`
Now, radius `=sqrt((-1)^(2)+(-2)^(2)+20)`
`=sqrt(1+4+20)=5`
`therefore ` Area of circle `=pir^(2)`
`=25pi"sq unit"`