K. C. Sinha Solutions for Chapter: Circle, Exercise 2: 3.2

Find the equation of the circle with centre $\left(-1,-2\right)$ and diameter $25$ units.

Find the centre and radius of the circle $\frac{1}{2}\left(x^2+y^2\right)+x\cos \theta +y\sin \theta -4=0$.

Find the equation of the circles passing through the following three points.

$\left(1,0\right),\left(0,1\right)$ and $\left(-1,0\right)$

Find the equation of the circle concentric with the circle $x^2+y^2-4x-6y-9=0$ and passing through the point $\left(-4,-5\right)$.

Find the Cartesian equations of the following curves whose parametric equations are :

$x=1+3\cos \theta , y=2-3\sin \theta$

Find the Cartesian equations of the following curves whose parametric equations are :

$x=\cos \theta +\sin \theta , y=\sin \theta -\cos \theta$

Find the Cartesian equations of the following curves whose parametric equations are :

$x=\frac{20t}{4+t^2}, y=\frac{5\left(4-t^2\right)}{4+t^2}$

Show that $x=a\cos \theta -b\sin \theta$ and $y=a\sin \theta +b\cos \theta$ represent a circle where $\theta$ is the parameter.