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

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 and has a slope equal to $\frac{3}{4},$ then the coordinates of the centre of $C_2$ are

For the circles $x^2+y^2-10x+16y+89-r^2=0$ and $x^2+y^2+6x-14y+42=0$ which of the following is/are trüe?

Which of the following statement $\left(s\right)$ is/are correct with respect to the circles $S_1\equiv x^2+y^2-4=0$ and $S_2\equiv x^2+y^2-2x-4y+4=0?$

Two circles, each of radius $5$ units, touch each other at $(1, 2).$ If the equation of their common tangent is $4x+3y=10.$ The equations of the circles are

$x^2+y^2=a^2$ and $(x-2a{)}^2+y^2=a^2$ are two equal circles touching each other. Find the equation of circle (or circles) of the same radius touching both the circles.

The circle $x^2+y^2-2x-3ky-2=0$ passes through two fixed points, $(k$ is the parameter)

Curves $a{x}^2+2hxy+b{y}^2-2gx-2fy+c=0$ and $a^{\text{'}}{x}^2-2hxy+\left(a^{\text{'}}+a-b\right)y^2-2g^{\text{'}}x-2f^{\text{'}}y+c=0$ intersect at four concyclic points $\mathrm{A},\mathrm{B},\mathrm{C}$ and $D$. If $P$ be the point $\left(\frac{g^{\text{'}}+g}{a^{\text{'}}+a},\frac{f^{\text{'}}+f}{a^{\text{'}}+a}\right)$, then which of the following is/are true $?$

Set of values of $m$ for which a chord of slope $m$ of the circle $x^2+y^2=4$ touches parabola $y^2=4x$, may lie in interval