A circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ passing through (4, 2) is concentric to the circle $x^{2} + y^{2} - 2 x + 4 y + 20 = 0,$ then the value of c will be

-4

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

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

Open in App

Solution

The correct option is A -4
Circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is concentric with $x^{2} + y^{2} - 2 x + 4 y + 20 = 0.$ Therefore centre is (1, -2) and radius
$= \sqrt{g^{2} + f^{2} - c} = \sqrt{(1 - 4)^{2} + (- 2 + 2)^{2}} \Rightarrow c = - 4.$

Suggest Corrections

Similar questions

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

x^{2} + y^{2} - 2 x + 4 y + 20 = 0,

(4, - 2)

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

x^{2} + y^{2} - 2 x + 4 y + 20 = 0

c

(2, - 1)

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

x^{2} + y^{2} + 4 x - 6 y + 3 = 0

c

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

x^{2} + y^{2} + 2 g x + 2 f y + k = 0

k

(- 3, 2)

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

x^{2} + y^{2} + 6 x + 8 y - 5 = 0

Join BYJU'S Learning Program