S L Loney Solutions for Chapter: The Circle, Exercise 3: EXAMPLES XIX

Find the length of tangent to the circle $2x^2+2y^2=3$ from the point $\left(-2, 3\right)$.

Find the length of the tangents drawn to the circle $3x^2+3y^2-7x-6y=12$ from the point $\left(6, -7\right)$.

Find the length of tangents drawn to the circle $x^2+y^2+2bx-3b^2=0$ from the point $\left(a+b, a-b\right)$.

Given the three circles, $x^2+y^2-16x+60=0, 3x^2+3y^2-36x+81=0$ and, $x^2+y^2-16x-12y+84=0$.

Find $\left(1\right)$, the point from which the tangents to them are equal in length and $\left(2\right)$, this length.

Given the three circles $x^2+y^2-16x+60=0, 3x^2+3y^2-36x+81=0$ and $x^2+y^2-16x-12y+84=0$. Find the point from which tangents to them are equal in length, and this length.

The distances from the origin of the centers of three circles $x^2+y^2-2\lambda x=c^2$ (where $c$, is a constant and $\lambda$, a variable) are in geometrical progression. Prove that the lengths of the tangents drawn to them from any point on the circle, $x^2+y^2=c^2$, are also in geometrical progression.

Find the equation to the pair of tangents drawn from the point $(11, 3)$, to the circle $x^2+y^2=65$.

Find the equation to the pair of tangents drawn from the point $\left(4, 5\right)$, to the circle $2x^2+2y^2-8x+12y+21=0$.