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)

$x^2 + y^2 = a^2 + b^2$

Answer 2

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 $x^2 + y^2 = (a^2 + b^2)$