Equation of Family of Circles Passing through Point of Intersection of Two Circles

Q. The equation of the circle passing through the point (–2, 4) and through the points of intersection of the circle $x^2+y^2-2x-6y+6=0$ and the line 3x + 2y - 5 = 0, is

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

Q.

The equation of the circle passing through $\left(1,1\right)$ and the points of intersection of $x^2+y^2+13x-3y=0$ and $2x^2+2y^2+4x-7y-25=0$ is

1. $4x^2+4y^2+30x-10y-25=0$

2. $4x^2+4y^2+30x-13y-25=0$

3. $4x^2+4y^2-17x-10y+25=0$

4. None of these

Q. The equation of the circle passing through (1, 1) and the points of intersection of $x^2+y^2+13x-3y=0$ and $2x^2+2y^2+4x-7y-25=0$ is

1. $x^2+y^2+15x-13y-25=0$
2. $2x^2+2y^2+25x-13y-30=0$
3. $4x^2+4y^2+30x-13y-25=0$
4. $4x^2+4y^2+25x-13y-30=0$

Q. If one end of the diameter of the circle $x^2+y^2-8x-4y+c=0$ is $(-3,2)$ then other co-ordinate is

1. $(6,2)$
2. $(5,3)$
3. $(1,-8)$
4. $(11,2)$

Q. The equation of the image of the circle $x^2+y^2+16x-24y+183=0$ along the line mirror $4x+7y+13=0$ is:

1. $x^2+y^2+32x-4y+235=0$
2. $x^2+y^2+32x+4y-235=0$
3. $x^2+y^2+32x-4y-235=0$
4. $x^2+y^2+32x+4y+235=0$

Q.

Find the equation of family of circles through the intersection of $x^2+y^2-6x+2y+4=0$ and $x^2+y^2+2x-4y-6=0$ whose center lies on $y=x.$

1. 

2. 

3. 

4. 

Q.

Find the equation of family of circles passing through the point of intersection of the circles $x^2+y^2-2x-4y-4=0$ and $x^2+y^2-10x-12y+40=0$ and whose radius is 4.

1. $x^2+y^2+2y+15=0$

2. $2x^2+2y^2-18x-22y+69=0$

3. $x^2+y^2-2y-15=0$

4. $x^2+y^2-18x-22y+69=0$

Q.

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

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

2. $3(x^2+y^2)+4x-4y-3=0$

3. $x^2+y^2-x-2y=0$

4. $3(x^2+y^2)+4(x+y)-3=0$

Q. The equation of the circle passing through (1, 1) and the points of intersection of $x^2+y^2+13x-3y=0$ and $2x^2+2y^2+4x-7y-25=0$ is

1. $2x^2+2y^2+25x-13y-30=0$
2. $4x^2+4y^2+30x-13y-25=0$
3. $x^2+y^2+15x-13y-25=0$
4. $4x^2+4y^2+25x-13y-30=0$

Q. The equation of the image of the circle $x^2+y^2-6x-4y+12=0$ by the line mirror $x+y-1=0$ is

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

Q.

Find the equation of family of circles through the intersection of $x^2+y^2-6x+2y+4=0$ and $x^2+y^2+2x-4y-6=0$ whose center lies on $y=x.$

1. $x^2+y^2-\frac{10}{7}x-\frac{10}{7}y-\frac{12}{7}=0$

2. $x^2+y^2+\frac{10}{7}x+\frac{10}{7}y-\frac{12}{7}=0$

3. $x^2+y^2-\frac{10}{7}x+\frac{10}{7}y+\frac{12}{7}=0$

4. $x^2+y^2+\frac{10}{7}x+\frac{10}{7}y+\frac{12}{7}=0$

Q. The equation of the circle passing through the point (–2, 4) and through the points of intersection of the circle $x^2+y^2-2x-6y+6=0$ and the line 3x + 2y - 5 = 0, is

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