Question

Find the equation of a circle drawn on the diagonal of the rectangle as its diameter, whose sides are along the lines $x=5,x=-2,y=3$ and $y=-1$.

Answer 1

Equation of Diagonals

$y-3=\frac{-1-3}{5+2}(x+2)$

$\Rightarrow y-3=\frac{-4}{7}(x+2)$

$\Rightarrow 7y-21=-4x-8$

$\Rightarrow 4x+7y=13$.....(i)

$y+1=\frac{3+1}{5+2}(x+2)$

$\Rightarrow 7y+7=4x+8$

$\Rightarrow 4x-7y=-1$.....(ii)

(i)+(ii)

$8x=12$

$\therefore x=\frac{3}{2}$

$4^2\times \frac{3}{2}+1=7y$

$\therefore y=1$

$(\frac{3}{2},1)$

Equation of circles is ${\left(x\frac{-3}{2}\right)}^2+(y-1{)}^2=\frac{65}{4}$