The value of k so that ${x^2} + {y^2} + kx + 4y + 2 = 0$ and $2({x^2} + {y^2}) - 4x - 3y + k = 0$ cut orthogonally is
The value of k so that ${x^2} + {y^2} + kx + 4y + 2 = 0$ and $2({x^2} + {y^2}) - 4x - 3y + k = 0$ cut orthogonally is
- A
$\frac{{10}}{3}$
- B
$\frac{{ - 8}}{3}$
- C
$\frac{{ - 10}}{3}$
- D
$\frac{8}{3}$
Similar Questions
The value of $\lambda $, for which the circle ${x^2} + {y^2} + 2\lambda x + 6y + 1 = 0$, intersects the circle ${x^2} + {y^2} + 4x + 2y = 0$ orthogonally is
The value of $\lambda $, for which the circle ${x^2} + {y^2} + 2\lambda x + 6y + 1 = 0$, intersects the circle ${x^2} + {y^2} + 4x + 2y = 0$ orthogonally 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
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 intercept on the line $y = x$ by the circle ${x^2} + {y^2} - 2x = 0$ is $AB$ . Equation of the circle with $AB$ as a diameter is
The intercept on the line $y = x$ by the circle ${x^2} + {y^2} - 2x = 0$ is $AB$ . Equation of the circle with $AB$ as a diameter is
- [IIT 1996]
The number of direct common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 -8x -8y + 7 = 0$ , is
The number of direct common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 -8x -8y + 7 = 0$ , is
The equation of the circle through the points of intersection of ${x^2} + {y^2} - 1 = 0$, ${x^2} + {y^2} - 2x - 4y + 1 = 0$ and touching the line $x + 2y = 0$, is
The equation of the circle through the points of intersection of ${x^2} + {y^2} - 1 = 0$, ${x^2} + {y^2} - 2x - 4y + 1 = 0$ and touching the line $x + 2y = 0$, is