Question

The sides of a rectangle are given by $x = \pm \, a$ and $y = \pm \, b$. The equation of the circle passing through the vertices of the rectangle is

• A. $x^2 + y^2 = a^2$
• B. $x^2 + y^2 = a^2 + b^2 $
• C. $x^2 + y^2 = a^2 - b^2 $
• D. $\left(x -a\right)^{2}+ \left(y-b\right)^{2} = a^{2} + b^{2} $

Answer 1

Answer: (B)

Given sides of rectangle are
$x=\pm a$ and $ y=\pm b $
$\therefore $ Centre of circle $=(0,0)$
and radius of circle $=\sqrt{a^{2}+b^{2}}$

$\therefore $ Equation of circle
$x^2 + y^2 = (a^2 + b^2)$