If the circles ${x^2} + {y^2} + 2x + 2ky + 6 = 0$ and ${x^2} + {y^2} + 2ky + k = 0$ intersect orthogonally, then $k$ is
If the circles ${x^2} + {y^2} + 2x + 2ky + 6 = 0$ and ${x^2} + {y^2} + 2ky + k = 0$ intersect orthogonally, then $k$ is
- [IIT 2000]
- A
$2$ or $ - \frac{3}{2}$
- B
$-2$ or $\frac{3}{2}$
- C
$2$ or $\frac{3}{2}$
- D
-$2$ or -$\frac{3}{2}$
Similar Questions
The co-axial system of circles given by ${x^2} + {y^2} + 2gx + c = 0$ for $c < 0$ represents
The co-axial system of circles given by ${x^2} + {y^2} + 2gx + c = 0$ for $c < 0$ represents
The centre of the circle, which cuts orthogonally each of the three circles ${x^2} + {y^2} + 2x + 17y + 4 = 0,$ ${x^2} + {y^2} + 7x + 6y + 11 = 0,$ ${x^2} + {y^2} - x + 22y + 3 = 0$ is
The centre of the circle, which cuts orthogonally each of the three circles ${x^2} + {y^2} + 2x + 17y + 4 = 0,$ ${x^2} + {y^2} + 7x + 6y + 11 = 0,$ ${x^2} + {y^2} - x + 22y + 3 = 0$ is
For the given circles ${x^2} + {y^2} - 6x - 2y + 1 = 0$ and ${x^2} + {y^2} + 2x - 8y + 13 = 0$, which of the following is true
For the given circles ${x^2} + {y^2} - 6x - 2y + 1 = 0$ and ${x^2} + {y^2} + 2x - 8y + 13 = 0$, which of the following is true
Choose the correct statement about two circles whose equations are given below
$x^{2}+y^{2}-10 x-10 y+41=0$
$x^{2}+y^{2}-22 x-10 y+137=0$
Choose the correct statement about two circles whose equations are given below
$x^{2}+y^{2}-10 x-10 y+41=0$
$x^{2}+y^{2}-22 x-10 y+137=0$
- [JEE MAIN 2021]
In the figure shown, radius of circle $C_1$ be $ r$ and that of $C_2$ be $\frac{r}{2}$ , where $r= \frac {1}{3} PQ,$ then length of $AB$ is (where $P$ and $Q$ being centres of $C_1$ $\&$ $C_2$ respectively)
In the figure shown, radius of circle $C_1$ be $ r$ and that of $C_2$ be $\frac{r}{2}$ , where $r= \frac {1}{3} PQ,$ then length of $AB$ is (where $P$ and $Q$ being centres of $C_1$ $\&$ $C_2$ respectively)