Embibe Experts Solutions for Exercise 14: Assignment

Find the length of major and minor axis, co-ordinates of the vertices and the foci, eccentricity and length of the latus rectum of the ellipse $y^2+36x^2=36$

Find the equation of the parabola which is symmetric about the $y$-axis, has its vertex at $(0, 0)$ and passes through the point $(4, -2).$

If $x^2-6y^2=6$ represents the equation of a hyperbola, then find its eccentricity.

Find the co-ordinates of a point on the parabola $y^2=16x$ whose focal distance is $8$ units.

Find the equation of the ellipse if its eccentricity is $\frac{\sqrt{13}}{7}$ and co-ordinates of the foci are $(0, \pm 2\sqrt{13}).$

If the eccentricity of an ellipse is $\frac{1}{6}th$ of the distance between the foci and distance between the foci is equal to $4\sqrt{2}$ units, then find the length of the latus rectum of the ellipse.

Find the equation of the hyperbola with foci $(\pm 5\sqrt{2}, 0)$ and the transverse axis is of length $14$ units.

Find the equation of the hyperbola whose foci are at $(\pm 3\sqrt{10}, 0)$ and passes through the point $(-9, 0).$