General Equation of Circle S=0

Q.

The center of a circle passing through the points $\left(0,0\right),\left(1,0\right)$ and touching the circle $x^2+y^2=9$ is

1. $\left(\frac{3}{2},\frac{1}{2}\right)$

2. $\left(\frac{1}{2},\frac{3}{2}\right)$

3. $\left(\frac{1}{2},\frac{1}{2}\right)$

4. $\left(\frac{1}{2},-2^{1/2}\right)$

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. 1

3. 0

4. None of these

Q.

A circle passes through the points $(0,0)$ and $(0,1)$ also touches the circle $x^2+y^2=16$.

The radius of the circle is

1. $1$

2. $2$

3. $3$

4. $4$

5. $5$

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. (2, 29/100)

2. (-2, 29/10)
   

3. (29/10, 2)
   

4. none of these

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. 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?
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