Embibe Experts Solutions for Chapter: Circle, Exercise 1: WBJEE 2020

The equation of circle of radius $\sqrt{17}$ units, with centre on the positive side of $x$-axis and through the point $\left(0, 1\right)$ is

A variable line passes through the fixed point $(\alpha , \beta )$. The locus of the foot of the perpendicular from the origin on the line is

A variable circle passes through the fixed point $A(p, q)$ and touches $X -$axis. The locus of the other end of the diameter through $A$ is

If one of the diameter of the circle, given by the equation $x^2+y^2+4x+6y-12=0,$ is a chord of a circle $S,$ whose centre is $(2,-3),$ the radius of $S$ is

The angle between a pair of tangents drawn from a point $P$ to the circle $x^2+y^2+4x-6y+9{\sin }^2\alpha +13{\cos }^2\alpha =0$ is $2\alpha$. The equation of the locus of the point $P$ is

A chord $AB$ is drawn from the point $A(0, 3)$ on the circle $x^2+4x+(y-3{)}^2=0,$ and is extended to $M$ such that $AM=2 AB$. The locus of $M$ is

Let $A$ be the centre of the circle $x^2+y^2-2x-4y-20=0.$ Let $B(1, 7)$ and $D(4,-2)$ be two points on the circle such that tangents at $B$ and $D$ meet at $C$. The area of the quadrilateral $ABCD$ is

The locus of the centre of the circles which touch both the circles $x^2+y^2=a^2$ and $x^2+y^2=4ax$ externally is