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

A circle of constant radius $r$ passes through the origin $O,$ and cuts the axes at $A$ and $B.$ The locus of the foot of the perpendicular from $O$ to $AB$ is ${\left(x^2+y^2\right)}^k=4r^2{x}^2{y}^2,$ then the value of $k$ is

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

A triangle has two of its sides along the axes, its third side touches the circle $x^2+y^2-4x-4y+4=0$ locus of circumcentre of triangle is

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

Let the tangent to the circle $x^2+y^2=25$ at the point $R(3,4)$ meet $x$ -axis and $y$-axis at point $P$ and $Q$, respectively. If $r$ is the radius of the circle passing through the origin $O$ and having centre at the incentre of the triangle $OPQ,$ then $r^2$ is equal to

A circle cutting the circle $x^2+y^2=4$ orthogonally and having its centre on the line $2x-2y+9=0,$ passes through two fixed points. These points are