Subject Experts Solutions for Chapter: Circle, Exercise 1: Practice Exercise

Consider the following circles:

$\mathrm{I}.$ $x^2+y^2+4x-6y-12=0$

$\mathrm{II}.$ $x^2+y^2-12x-14y+60=0$

$\mathrm{III}.$ $x^2+y^2-10x+8y+18=0$

Which of the above circles has equal area?

What is the radius of the circle touching $X$-axis at $\left(3,0\right)$ and $Y$-axis at $(0,3)?$

The angle subtended at the centre of a circle of radius $3 \mathrm{cm}$ by an arc of length $1 \mathrm{cm}$ is 

Which one of the following points lies inside a circle of radius $6$ and centre at $(3,5)?$

The radius of the circle $x^2+y^2+x+c=0$ passing through the origin is

A straight line $x=y+2$ touches the circle $4\left(x^2+y^2\right)=r^2.$ The value of $r$ is 

If the centre of the circle passing through the origin is $(3,4),$ then the intercepts cut-off by the circle on $X$-axis and $Y$-axis, respectively are

If a circle of radius $b$ units with center at $(0,b)$ touches the line $y=x-\sqrt{2},$ then what is the value of $b?$