Maharashtra Board Solutions for Chapter: Circle, Exercise 4: MISCELLANEOUS EXERCISE - 6

Find the equation of locus of the point of intersection of perpendicular tangents drawn to the circle $\mathrm{x}=5\mathrm{cos\theta }$ and $\mathrm{y}=5\mathrm{sin\theta }$

Find the equation of the circle concentric with $x^2 + y^2 – 4x + 6y = 1$and having radius $4$ units.

Find the lengths of the intercepts made on the co-ordinate axes, by the circle $x^2 + y^2 – 5x + 13y – 14 = 0$

Find the length of the tangent segment drawn from the point $(5,3)$to the circle ${\mathrm{x}}^{2 }+{\mathrm{y}}^2+10\mathrm{x}–6\mathrm{y}–17=0$.

If the tangent at $(3,–4)$ to the circle ${\mathrm{x}}^{2 }+{\mathrm{y}}^2=25$ touches the circle ${\mathrm{x}}^2+{\mathrm{y}}^2+8\mathrm{x}–4\mathrm{y}+\mathrm{c}=0$, find $c$.

Find the equations of the tangents to the circle $x^2+y^2=16$ with slope $-2$.

Find the equations of the tangents to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=4$ which are parallel to $3\mathrm{x}+2\mathrm{y}+1=0$.

Tangents to the circle${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2$with inclinations, ${\theta }_1$ and ${\theta }_2$ intersect in $\mathrm{P}$. Find the locus of $\mathrm{P}$ such that

i) $\tan {\mathrm{\theta }}_1+\tan {\mathrm{\theta }}_2=0$

ii) $\cot {\mathrm{\theta }}_1+\cot {\mathrm{\theta }}_2=5$

iii) $\cot {\mathrm{\theta }}_1 . \cot {\mathrm{\theta }}_2 = \mathrm{c}$.