General Equation of Circle S=0

Q. From the point A (0, 3) on the circle $x^2+4x+(y-3{)}^2=0$ a chord AB is drawn and extended to a point M such that AM =2AB. The equation of the locus of M is___

1. $x^2+y^2-6x+8y+9=0$
2. $x^2+y^2-8x+6y+9=0$
3. $x^2+y^2+6x-8y+9=0$
4. $x^2+y^2+8x-6y+9=0$

Q.

Let $\varphi (x,y)=0$ be the equation of a circle, If $\varphi (0,\lambda )=0$ has equal roots $\lambda =2,2$ and $\varphi (\lambda ,0)=0$ has roots $\lambda =\frac{4}{5},5,$ then the roots of the circle is

1. (29/10, 2)
   

2. (-2, 29/10)
   

3. None of these

4. (2, 29/100)

Q. For how many values of p does the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points?
___

Q. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

1. (a, b)
2. (b, a)
3. $(\frac{a}{2},\frac{b}{2})$
4. $(\frac{b}{2},\frac{a}{2}).$

Q. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

1. (a, b)
2. (b, a)
3. 
4. 

Q. If the equation $\frac{K(x+1{)}^2}{3}+\frac{(y+2{)}^2}{4}=1$ represents a circle, then K =

1. 3/4
2. 12
3. 1
4. 4/3

Q.

If $(m_i,\frac{1}{m_i})$, i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_1{m}_2{m}_3{m}_4$ is

1. -1

2. 0

3. None of these

4. 1

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

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

Q.

$(2+2\lambda +\mu )x^2+(1+2\lambda +2\mu )y^2+(3+5\lambda +3\mu )xy$

$-(16+14\lambda +11\mu )x-(10+13\lambda +17\mu )+(24+20\lambda +30\mu )=0$ is an equation of circle only when

1. 

2. 

3. 

4. 

Q. If the equation $\frac{K(x+1{)}^2}{3}+\frac{(y+2{)}^2}{4}=1$ represents a circle, then K =

1. 3/4
2. 1
3. 4/3
4. 12

Q. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

1. (a, b)
2. (b, a)
3. $(\frac{a}{2},\frac{b}{2})$
4. $(\frac{b}{2},\frac{a}{2}).$

Q.

Which of the following equations represents a circle with centre $(g,f)$ and radius $\sqrt{g^2+f^2+c}$ ?

1. $x^2+y^2+2gx+2fy+c=0$

2. $x^2+y^2-2gx-2fy+c=0$

3. $x^2+y^2+2gx+2fy-c=0$

4. $x^2+y^2-2gx-2fy-c=0$