Embibe Experts Solutions for Chapter: Circle, Exercise 3: Exercise-3

If $P$ and $Q$ are the points of intersection of the circles $x^2+y^2+3x+7y+2p-5=0$ and $x^2+y^2+2x+2y-p^2=0$, then there is a circle passing through $P, Q$ and $\left(1,1\right)$ for

The circle $x^2+y^2=4x+8y+5$ intersects the line $3x-4y=m$ at two distinct points if

The length of the diameter of the circle which touches the $x$-axis at the point $\left(1,0\right)$ and passes through the point $\left(2,3\right)$ is

The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point 

Let $C$ be the circle with centre at $(1,1)$ and radius $=1$. If $T$ is the circle centered at $(0, y)$ passing through the origin and touching the circle $C$ externally, then the radius of $T$ is equal to

If a variable line, $3x+4y-\lambda =0$ is such that the two circles $x^2+y^2-2x-2y+1=0$ and $x^2+y^2-18x-2y+78=0$ are on its opposite sides, then the set of all values of $\lambda$ is the interval:

Match the information given in the three columns of the following table (appropriately).

For $a=\sqrt{2},$ if a tangent is drawn to a suitable conic (Column $1$ ) at the point of contact $(-1,1),$ then which of the following options is the only CORRECT combination for obtaining its equation?

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ having centre at $\left(0,3\right)$ is