Embibe Experts Solutions for Exercise 1: Exercise

Find the pair tangents drawn from $\left(3,2\right)$ to the circle $x^2+y^2-6x+4y-2=0$.

Find the pole of the straight line $2 x+3 y-4=0$ with respect to the circle $x^2+y^2+4x+6y+3=0$

The polars of two points $A(2,4)$ and $B(3,5)$ with respect to the circle $x^2+y^2+2gx+2fy+c=0$ intersect at $C$ then find the polar of $C$ with respect to the circle.

The polars of two points $A(3,-2)$ and $B(5,4)$ with respect to the circle $x^2+y^2+2gx+2fy+c=0$ intersect at $C$ then find the polar of $C$ with respect to the circle.

Find the equation of the normal to the circle $x^2+y^2=10$ in the parametric form, where the parameter is $\theta =30°$.

Suppose that the chord joining the points $\theta$ and $\varphi$ on the circle $x^2+y^2=r^2$ intersects the $x$-axis at $(h,0)$. Show that $\frac{h}{r}= \frac{\cos \left(\frac{\theta -\varphi }{2}\right)}{\cos \left(\frac{\theta +\varphi }{2}\right)}$.

 Find the length of the $x$-intercept and $y$-intercept made by the circle $x^2+y^2-8x-4y-6=0$ with the co-ordinate axes.

 Find the length of the $x$-intercept and $y$-intercept made by the circle $x^2+y^2-16x-16y-36=0$ with the co-ordinate axes.