If (-3, 2) lies on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ which is concentric with the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ , then $c$ is equal to

11

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

- 11

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

24

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

100

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

Open in App

Solution

The correct option is C $- 11$
Equation of family of concentric circle to the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ is
$x^{2} + y^{2} + 6 x + 8 y + λ = 0$
which is similar to $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ .
Thus, the point $(- 3, 2)$ lies on the circle
$x^{2} + y^{2} + 6 x + 8 y + c = 0$
$\Rightarrow (- 3)^{2} + (2)^{2} + 6 (- 3) + 8 (2) + c = 0$
$\Rightarrow 9 + 4 - 18 + 16 + c = 0$
$\Rightarrow c = - 11$

Suggest Corrections

Similar questions

If (-3, 2) lies on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ which is concentric with the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ , then c=

Q. If

(- 3, 2)

lies co the circle

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

, which is concentric with the circle

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

, then c is equal to

If the circles $x^{2} + y^{2} - 6 x - 8 y - 24$ = 0 and $3 x^{2} + 3 y^{2} + 2 g x + 2 f y + 0$ = 0 are concentric then (g.f)

Q. If the circle

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

cuts each of the circles

x^{2} + y^{2} - 4 = 0, x^{2} + y^{2} - 6 x - 8 y + 10 = 0

and

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

at the extremities of a diameter, then

Q. The condition if the equation of a circle concentric with the circle

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

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

, where

k

is a constant.

Join BYJU'S Learning Program

If (-3, 2) lies on the circle x2+y2+2gx+2fy+c=0 which is concentric with the circle x2+y2+6x+8y−5=0, then c is equal to

The correct option is C −11Equation of family of concentric circle to the circle x2+y2+6x+8y−5=0 isx2+y2+6x+8y+λ=0which is similar to x2+y2+2gx+2fy+c=0.Thus, the point (−3,2) lies on the circlex2+y2+6x+8y+c=0⇒(−3)2+(2)2+6(−3)+8(2)+c=0⇒9+4−18+16+c=0⇒c=−11

If (-3, 2) lies on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ which is concentric with the circle $x^{2} + y^{2} + 6 x + 8 y - 5 = 0$ , then $c$ is equal to