Embibe Experts Solutions for Chapter: Circle, Exercise 1: Level 1

The equation of the circle which passes through the points $\left(1,0\right),\left(0,-6\right)$ and $\left(3,4\right)$ is

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 $b?$

The line $x\sin \alpha -y\cos \alpha =a$ touches the circle $x^2+y^2=a^2$. Then,

If a chord of a circle $x^2+y^2=4$ with one extremity at $\left(1,\sqrt{3}\right)$ subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be

If the line $ax+by=2, (a\ne 0)$ touches the circle $x^2+y^2-2x=3$ and is normal to the circle $x^2+y^2-4y=6$, then $a+b$ is equal to

The centre of the circle $(x-\alpha {)}^2+(y-\beta {)}^2=9$ lies on the straight line $x=y$ and the circle touches the circle $x^2+y^2=1$ externally. What are the values of $\alpha , \beta ?$

If one of the diameters of the circle $x^2+y^2-2x-6y+6=0$ is a chord of another circle ${}^{\text{'}}C^{\text{'}}$, whose center is at $\left(2,1\right)$, then its radius is_____.

The minimum distance between any two points $P_1$ and $P_2$ while considering point $P_1$ on one circle and point $P_2$ on the other circle for the given circles' equations

$x^2+y^2-10x-10y+41=0$

$x^2+y^2-24x-10y+160=0$ is ________