Amit M Agarwal Solutions for Chapter: Circle, Exercise 4: Entrances Gallery

The centre of a circle which cuts $x^2+y^2+6x-1=0, x^2+y^2-3y+2=0$ and $x^2+y^2+x+y-3=0$ orthogonally is

The line segment joining the points $\left(4,7\right)$ and $\left(-2,-1\right)$ is a diameter of a circle. If the circle intersects $x$-axis at $A$ and $B$, then $AB$ is equal to

The distance of the midpoint of the line joining two points $\left(4,0\right)$ and $\left(0,4\right)$ from the centre of the circle $x^2+y^2=16$ is

The equation of family of circles with centre at $\left(h,k\right)$ touching $x$-axis, is given by

The straight line $x+y-1=0$ meets the circle $x^2+y^2-6x-8y=0$ at $A$ and $B$. Then, the equation of the circle of which $AB$ is a diameter, is

The equation of normal of $x^2+y^2-2x+4y-5=0$ at $\left(2,1\right)$ is

The equation of the chord of the circle $x^2+y^2=81$ which is bisected at the point $\left(-2,3\right)$ is

If the two circles ${\left(x+7\right)}^2+{\left(y-3\right)}^2=36$ and ${\left(x-5\right)}^2+{\left(y+2\right)}^2=49$ touch each other externally then the point of contact is