G Tewani Solutions for Chapter: Circles, Exercise 5: DPP

Tangents $PA$ and $PB$ are drawn to the circle $x^2+y^2=8$ from any arbitrary point $P$ on the line $x+y=4.$ The locus of the mid-point of chord of contact $AB$ is

The locus of the center of a circle which cuts a given circle orthogonally and also touches a given straight line is a

A circle with radius $a$ and the center on the $y$-axis slides along the $y$-axis. If a variable line through $\left(a, 0\right)$ cuts the circle at points $P$ and $Q$, then the point of intersection of the tangents to the circle at $P$ and $Q$ will lie in the region defined by

The points at which two circles with unequal radii subtend equal angles lies on

The locus of the center of the circle which bisects the circumference of the circles $x^2+y^2=4$ and $x^2+y^2-2x+6y+1=0$ is

Locus of the centre of a family of circles cutting the family of circles $x^2+y^2+4x\left(\lambda -\frac{3}{2}\right)+3y\left(\lambda -\frac{4}{3}\right)-6\left(\lambda +2\right)=0$ is

Let $Q$ is any point on the circle $x^2+y^2=9$. $QN$ is the perpendicular from $Q$ on the $x$-axis. Locus of the point of trisection of $QN$ is

Locus of the intersection of the two straight lines passing through $\left(1, 0\right)$ and $\left(-1, 0\right)$, respectively, and including an angle of $45°$ can be a circle with