If $y = 2 x$ is a chord of the circle $x^{2} + y^{2} - 10 x = 0$ , find the equation of a circle with this chord as diameter.

Open in App

Solution

Points of intersection is given by

$x^{2} + (2 x)^{2} - 10 x = 0$

$⟹ 5 x^{2} - 10 x = 0$

$⟹ x = 0, 2 ⟹ y = 0, 4$

A $(0, 0)$ and B $(2, 4)$ are ends of diameter of a circle whose equation is given by

$(x - 0) (x - 2) + (y - 0) (y - 4) = 0$

$x^{2} + y^{2} - 2 x - 4 y = 0$

Suggest Corrections

Similar questions

y = 2 x

x^{2} + y^{2} - 10 = 0

y = 2 x

x^{2} + y^{2} - 10 x = 0

If y = 2x is a chord of the circle $x^{2} + y^{2} - 10 x = 0$ , find the equation of a circle with this chord as diameter.

Find the equation of ellipse whose foci are (2, 3) and (- 2, 3) and whose semi-minor axis is $\sqrt{5}$

y + 3 x = 0

x^{2} + y^{2} - 30 x = 0

x + y = 3

A B

x^{2} + y^{2} - 2 x + 4 y - 8 = 0,

A B

Join BYJU'S Learning Program