Dr. SK Goyal Solutions for Chapter: Circle, Exercise 6: INTRODUCTORY EXERCISE 4.6

Number of common real tangents that can be drawn to the circles $x^2+y^2-2x-2y=0$ and $x^2+y^2-8x-8y+14=0$ is

The circles whose equations are $x^2+y^2+c^2=2ax$ and $x^2+y^2+c^2-2by=0$ will touch one another externally, if:

If one of the circles $x^2+y^2+2ax+c=0$ and $x^2+y^2+2bx+c=0$ lies within the other, then :

If the circle $x^2+y^2+4x+22y+c=0$ bisects the circumference of the circle $x^2+y^2-2x+8y-d=0$, then $c+d$ is equal to:

The equation of the diameter of the circle $3\left(x^2+y^2\right)-2x+6y-9=0$ which is perpendicular to the line $2x+3y=12$ is:

Prove that the circles $x^2+y^2+2ax+2by=0$ and $x^2+y^2+2a_{1}x+2b_{1}y=0$ touch each other, if $a{b}_1=a_{1}b$.

Prove that the polar of the point $\left(p,q\right)$ with respect to the circle $x^2+y^2=a^2$ touches ${\left(x-c\right)}^2+{\left(y-d\right)}^2=b^2$, if $b^2\left(p^2+q^2\right)={\left(a^2-cp-dq\right)}^2$.

Find the values of $a$ and $b$ if the pole of the line $ax+by-1=0$ with respect to the circle $x^2+y^2+4x+7y+11=0$ is $\left(-\frac{7}{8},-\frac{11}{8}\right)$.