If the ratio of the lengths of tangents drawn from the point $(f,g)$ to the given circle ${x^2} + {y^2} = 6$ and ${x^2} + {y^2} + 3x + 3y = 0$ be $2 : 1$, then
If the ratio of the lengths of tangents drawn from the point $(f,g)$ to the given circle ${x^2} + {y^2} = 6$ and ${x^2} + {y^2} + 3x + 3y = 0$ be $2 : 1$, then
- A
${f^2} + {g^2} + 2g + 2f + 2 = 0$
- B
${f^2} + {g^2} + 4g + 4f + 4 = 0$
- C
${f^2} + {g^2} + 4g + 4f + 2 = 0$
- D
None of these
Similar Questions
Equation of the tangent to the circle, at the point $(1 , -1)$ whose centre is the point of intersection of the straight lines $x - y = 1$ and $2x + y= 3$ is
Equation of the tangent to the circle, at the point $(1 , -1)$ whose centre is the point of intersection of the straight lines $x - y = 1$ and $2x + y= 3$ is
- [JEE MAIN 2016]
Tangents are drawn from the point $(4, 3)$ to the circle ${x^2} + {y^2} = 9$. The area of the triangle formed by them and the line joining their points of contact is
Tangents are drawn from the point $(4, 3)$ to the circle ${x^2} + {y^2} = 9$. The area of the triangle formed by them and the line joining their points of contact is
- [IIT 1981]
The line $lx + my + n = 0$ is normal to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$, if
The line $lx + my + n = 0$ is normal to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$, if
Let the tangents at the points $A (4,-11)$ and $B (8,-5)$ on the circle $x^2+y^2-3 x+10 y-15=0$, intersect at the point $C$. Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to
Let the tangents at the points $A (4,-11)$ and $B (8,-5)$ on the circle $x^2+y^2-3 x+10 y-15=0$, intersect at the point $C$. Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to
- [JEE MAIN 2023]
The equation to the tangents to the circle ${x^2} + {y^2} = 4$, which are parallel to $x + 2y + 3 = 0$, are
The equation to the tangents to the circle ${x^2} + {y^2} = 4$, which are parallel to $x + 2y + 3 = 0$, are