Coaxial System

Q.

$x^2+y^2-4x+6y-12=0$ and $x^2+y^2+6x+18y+26=0$ __________.

1. Touch each other internally

2. Touch each other externally

3. One circle lies completely outside the other circle

4. One circle lies completely inside the other circle

Q.

If the two circles $x^2+y^2+2gx+2fy=0$ and $x^2+y^2+2g_{1}x+2f_{1}y=0$ touch each other then

1. $f{f}_1=g{g}_1$

2. $f{g}_1=f_1{g}_1$

3. (fg_1 = f_1g\)

4. $f^2+g^2=f_1^2+f_1^2$

Q. If the circles $x^2+y^2+2ax+2by+c=0$ and $x^2+y^2+2bx+2ay+c=0$ touch each other then

1. $(a-b{)}^2=2c$
2. $a+b=2c$
3. $(a+b{)}^2=2c$
4. $(a+b{)}^2=c$

Q.

$x^2+y^2-4x+6y-12=0$ and $x^2+y^2+6x+18y+26=0$ __________.

1. Touch each other internally

2. Touch each other externally

3. One circle lies completely outside the other circle

4. One circle lies completely inside the other circle

Q. The points on the curve $x{y}^2=1$ which are nearest to the origin, are

1. $[{\left(\frac{1}{2}\right)}^{1/3},\pm {\left(\frac{1}{2}\right)}^{-1/6}]$
2. $[{\left(\frac{1}{2}\right)}^{1/3},2^{-1/6}]$
3. $[2^{1/3},\pm {\left(\frac{1}{2}\right)}^{-1/6}]$
4. None of these

Q. The lengths of tangents from a fixed point to three circles of coaxial system are $t_1,t_2,t_3$ and if P, Q and R be the centres, then $QR{t}_1^2+RP{t}_2^2+PQ{t}_3^2$ is equal to

1. 1
2. 2
3. 3
4. \N