The equation of the circle having $(- 2, - 1)$ and $(2, 1)$ as the endpoints of its diameter is

$x^{2} - y^{2} = - 5$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$x^{2} + y^{2} = 5$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$x^{2} - y^{2} = 5$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$x^{2} + y^{2} = - 5$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$x^{2} + y^{2} = 5$

Equation of a circle when the end points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ of its diameter are given, is given by,

$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$

So, when $(- 2, 1)$ and $(4, - 1)$ are the end points of the diameter, equation of the circle would become:

$(x + 2) (x - 2) + (y + 1) (y - 1) = 0$

$⟹$ $x^{2} - 4 + y^{2} - 1 = 0$

$⟹$ $x^{2} + y^{2} - 5 = 0$

$⟹$ $x^{2} + y^{2} = 5$

Suggest Corrections

Similar questions

(6, - 3)

(2, - 1)

The equation of the circle having $(3, 3)$ and origin as the endpoints of its diameter is

The equation of the circle having $(6, 7)$ and $(4, 3)$ as the endpoints of its diameter is

The equation of the circle having $(4, 2)$ and $(2, - 12)$ as the end points of its diameter is

A (- 3, 9)

B (9, - 1)

Join BYJU'S Learning Program