Embibe Experts Solutions for Exercise 10: EXERCISE 13.3

Length of the latus-rectum of the ellipse represented by $x=3(\cos t+\sin t), y=4(\cos t-\sin t);$ is given by

Tangents are drawn to the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ at the ends of latus rectum. The area of quadrilateral so formed is (in sq. units)

If tangents are drawn to the ellipse $x^2+2y^2=2,$ then the locus of mid points of the intercept made by the tangents between the co-ordinate axes, is

If the line $px+qy=r$ intersects the ellipse $x^2+4y^2=4$ in points, whose eccentric angles differ by $\frac{\mathrm{\pi }}{3},$ then $r^2$ is equal to

Product of the perpendiculars drawn from the foci upon any tangent to the ellipse $3x^2+4y^2=12$ is

The line $lx+m y+n=0$ is a normal to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ if

If the normal to the ellipse $\frac{x^2}{14}+\frac{y^2}{5}=1$ at the point $\mathrm{\theta }$ intersects the curve again at the point $2\mathrm{\theta },$ then cos $\mathrm{\theta }$ is equal to

The equation of the director circle of the ellipse $4x^2+9y^2=36,$ is given by