Embibe Experts Solutions for Exercise 7: Assignment

Tangents and normal are drawn from a point $P(3, 1)$ to circle $C$ whose equation is $x^2+y^2-2x-2y+1=0.$ Let the points of contact of tangents be $T_i$ $\left(x_i, y_i\right),$ where $i=1, 2$ and feet of normals be $N_1$ and $N_2\left(N_1\right.$ is near $\left.P\right).$ Tangents are drawn at $N_1$ and $N_2$ and normals are drawn at $T_1$ and $T_2$

Let $C_1$ and $C_2$ be two concentric circles such that the radius of $C_2$ is double that of radius of $C_1.$ Tangents $PQ$ and $PR$ are drawn from a point on $C_2$ to $C_1$

Chords are drawn to the circle $x^2+y^2-2x-2y-8=0$ from the point $(-1, -1).$ If circle cuts off equal intercept on these chords and the line $3x+4y+3=0,$ then the equation of chord$\left(s\right)$ may be

The equation of a circle touching $x$-axis at $(-4, 0)$ and cutting off an intercept of $6$ units on $y$-axis can be

Let one of the vertices of the square circumseribing the circle $x^2+y^2-6x-4y+11=0$ be $(4, 2+\sqrt{3}).$ The other vertices of the square may be

If $x^2+y^2-2y-15+\lambda (2x+y-9)=0$ represents family of circles for different values of $\lambda ,$ then the equation of the circle$\left(s\right)$ along these circles having minimum radius is/are

The straight line $lx+my=1$ intersects $p{x}^2+2qxy+r{y}^2=s$ at $AB.$ Chord $AB$ subtends a right angle at the origin. If $lx+my=1$ is a tangent to a circle $x^2+y^2=a^2,$ then $a=$

Let the midpoint of the chord of contact of tangents drawn from $A$ to the circle $x^2+y^2=4$ be $M(1, -1)$ and the points of contact be $B$ and $C$