Embibe Experts Solutions for Exercise 1: Telangana Board-2018

Find the equation of the circle whose centre is $(-1,2)$ and which passes through the point $(5,6)$.

Find the area of the triangle formed by the normal at $(3,-4)$ to the circle $x^2+y^2-22x-4y+25=0$ with the coordinate axes.

Find the area of the triangle formed by the normal at $(3,-4)$ to the circle $x^2+y^2-22x-4y+25=0$ with the coordinate axes.

The line $y=mx+c$ and the circle $x^2+y^2=a^2$ intersect at $A$ and $B$. If $AB=2\lambda$, then show that : $c^2=\left(1+m^2\right)\left(a^2-{\lambda }^2\right)$

Show that, four common tangents can be drawn for the circles given by $x^2+y^2-14x+6y+33=0$ and $x^2+y^2+30x-2y+1=0$ and find the internal and external centres of similitude.

Find the length of the chord intercepted by the circle:

$x^2+y^2-x+3y-22=0$

on the line $y=x-3$.

Find the equation of a circle which passes through $\left(2,-3\right)$ and $\left(-4,5\right)$ and having the center on $4x+3y+1=0$.

Show that $x^2+y^2-6x-9y+13=0, x^2+y^2-2x-16y=0$ touch each other. Find the point of contact and the equation of common tangent at their point of contact.