Power of a Point

Q. If the power of point $(1,-2)$ with respect to $x^2+y^2=1$ is equal to the radius of a circle and $(3,2)$ is the centre of that circle, then the equation of that circle is

1. $x^2+y^2-6x-4y-3=0$
2. $x^2+y^2-6x-4y-5=0$
3. $x^2+y^2-6x-4y+3=0$
4. $x^2+y^2-6x-4y+5=0$

Q. If the power of point $(2,1)$ with respect to the circle $2x^2+2y^2-8x-6y+k=0$ is positive, then

1. $12<k<\infty$
2. $-12<k<12$
3. $12<k<\frac{25}{2}$
4. $12<k<25$

Q. If the power of point $(2,1)$ with respect to the circle $2x^2+2y^2-8x-6y+k=0$ is positive, then

1. $12<k<\infty$
2. $-12<k<12$
3. $12<k<\frac{25}{2}$
4. $12<k<25$

Q.

The radius of the circle S is same as the radius of $x^2+y^2-2x+4y-11=0$ and the centre of S is the centre of $x^2+y^2-2x-4y+11=0$ . Find the equation of S.

1. 

2. 

3. 

4. 

Q. Let the locus of foot of the perpendicular drawn from $(1,-2)$ to the family of lines $(3+\lambda )x+(3\lambda -2)y=8-\lambda$ is $s=0$. If the line's joining origin to the point of intersections of $s=0$ with the line $x+by=1$ makes an angle of ${60}^{\circ }$ then sum of all possible values of $b$ is

1. $\frac{3}{2}$
2. $\frac{-3}{2}$
3. $\frac{5}{2}$
4. $\frac{-5}{2}$

Q. The number of pairs $(a,b)$ of positive real numbers satisfying $a^4+b^4<1$ and $a^2+b^2>1$ is/are:

1. $1$
2. $2$
3. more than $2$
4. $0$

Q.

Find the value of λ if the point (3, 5) lies inside the circle $x^2+y^2+6x+\lambda y+5=0$

1. λ< 5

2. λ<-57/5

3. λ>5

4. λ<11

Q. Find the center-radius form of the equation of the circle with center $(4,0)$ and radius $7$

1. ${(x-4)}^2+y^2=49$
2. $x^2+{(y-4)}^2=7$
3. ${(x+4)}^2+y^2=49$
4. $x^2+{(y+4)}^2=7$

Q. If the power of point $(1,-2)$ with respect to $x^2+y^2=1$ is equal to the radius of a circle and $(3,2)$ is the centre of that circle, then the equation of that circle is

1. $x^2+y^2-6x-4y-3=0$
2. $x^2+y^2-6x-4y-5=0$
3. $x^2+y^2-6x-4y+3=0$
4. $x^2+y^2-6x-4y+5=0$

Q.

Find the value of λ if the point (3, 5) lies inside the circle $x^2+y^2+6x+\lambda y+5=0$

1. $\lambda <5$

2. $\lambda <\frac{-57}{5}$

3. $\lambda >5$

4. $\lambda <11$

Q. The values of $\lambda$ for which the circle $x^2+y^2+6x+5+\lambda (x^2+y^2-8x+7)=0$ dwindles into a point are

1. $1\pm \frac{\sqrt{2}}{3}$
2. $2\pm \frac{2\sqrt{2}}{3}$
3. $2\pm \frac{4\sqrt{2}}{3}$
4. $1\pm \frac{4\sqrt{2}}{3}$

Q. If the power of point $(2,1)$ with respect to the circle $2x^2+2y^2-8x-6y+k=0$ is positive, then

1. $12<k<\infty$
2. $-12<k<12$
3. $12<k<\frac{25}{2}$
4. $12<k<25$

Q.

Find the value of λ if the point (3, 5) lies inside the circle $x^2+y^2+6x+\lambda y+5=0$

1. $\lambda <5$

2. $\lambda <\frac{-57}{5}$

3. $\lambda >5$

4. $\lambda <11$

Q.

The power of P(1, 2) with respect to the circle $x^2+y^2+4x+2y+3$ = 0 is double the power of P with respect to $x^2+y^2+2x+y+k$ = 0 then the value of k is

1. 1

2. 0

3. 4

4. -1

Q. If the power of point $(1,-2)$ with respect to $x^2+y^2=1$ is equal to the radius of a circle and $(3,2)$ is the centre of that circle, then the equation of that circle is

1. $x^2+y^2-6x-4y-3=0$
2. $x^2+y^2-6x-4y-5=0$
3. $x^2+y^2-6x-4y+3=0$
4. $x^2+y^2-6x-4y+5=0$

Q.

The power of P(1, 2) with respect to the circle $x^2+y^2+4x+2y+3$ = 0 is double the power of P with respect to $x^2+y^2+2x+y+k$ = 0 then the value of k is

1. 1

2. 0

3. -1

4. 4

Q.

The power of (2, 1) with respect to the circle $2x^2+2y^2-8x-6y+k$ = 0 is positive if

1. 0<k<12

2. -12<k<12

3. k>12

4. k<12