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

Question

The sides of a rectangle are given by x = ± a and y = ± b. The equation of the circle passing through the vertices of the rectangle is (A) x2 + y2 = a2 (B) x2 + y2 = a2 + b2  (C) x2 + y2 = a2 - b2  (D) (x -a)2+ (y-b)2 = a2 + b2

Tardigrade Admin · Accepted Answer

Given sides of rectangle are x=± a and y=± b ∴ Centre of circle =(0,0) and radius of circle =√a2+b2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a3b0e92f38ac8292ba5c09bcd9ebee08-.png" /> ∴ Equation of circle x2 + y2 = (a2 + b2)

Q. 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

$x^{2} + y^{2} = a^{2}$

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

$x^{2} + y^{2} = a^{2} - b^{2}$

$(x - a)^{2} + (y - b)^{2} = a^{2} + b^{2}$

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

$∴$ Equation of circle
$x^{2} + y^{2} = (a^{2} + b^{2})$

Q. The sides of a rectangle are given by x=±a and y=±b. The equation of the circle passing through the vertices of the rectangle is

x2+y2=a2

x2+y2=a2+b2

x2+y2=a2−b2

(x−a)2+(y−b)2=a2+b2