Embibe Experts Solutions for Chapter: Circle, Exercise 2: EXERCISE-2

Let $f\left(x\right)=x^2+6x+1$ and $R$ denote the set of points $\left(x, y\right)$ in the coordinate plane such that $f\left(x\right)+f\left(y\right)\le 0$ and $f\left(x\right)-f\left(y\right)\le 0$. The area of $R$ is equal to -

A circle touches a straight line $fx+my+n=0$ and cuts the circle $x^2+y^2=9$ orthogonally. The locus of centres of such circles is

Equation $\frac{x-x_1}{\cos \theta }=\frac{y-y_1}{\sin \theta }=r$, may represents

If $r$ represent the distance of a point from origin $\& \theta$ is the angle made by line joining origin to that point from line $x$-axis, then $r=\left|\cos \theta \right|$ represents

If the circle $C_1:x^2+y^2=16$ intersects another circle $C_2$ of radius $5$ in such a manner that the common chord is of maximum length $8$ has a slope equal to $\frac{3}{4}$, then coordinates of centre of $C_2$ are

For the equation $x^2+y^2+2\lambda x+4=0$ which of the following can be true

If $y=c$ is a tangent to the circle $x^2+y^2-2x+2y-2=0$, then the value of $c$ can be:-

For the circles $S_1\equiv x^2+y^2-4x-6y-12=0$ and $S_2=x^2+y^2+6x+4y-12=0$ and the line $L\equiv x+y=0$