An ellipse is described by using an endless s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The length of the string used to draw an ellipse with pins at the foci is equal to the sum of the major axis and the distance between the foci.Giv

Vedclass · Accepted Answer

$6 + 2\sqrt{5}, 2\sqrt{5}$

Vedclass · Answer

(D) The length of the string used to draw an ellipse with pins at the foci is equal to the sum of the major axis and the distance between the foci.Given the major axis $2a = 6 \ cm$,so $a = 3 \ cm$.Given the minor axis $2b = 4 \ cm$,so $b = 2 \ cm$.The eccentricity $e$ is given by $e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{4}{9}} = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}$.The distance between the pins (foci) is $2ae = 2 	imes 3 	imes \frac{\sqrt{5}}{3} = 2\sqrt{5} \ cm$.The length of the string is $2a + 2ae = 6 + 2\sqrt{5} \ cm$.

An ellipse is described by using an endless string which is passed over two pins. If the axes are $6 \ cm$ and $4 \ cm$,the necessary length of the string and the distance between the pins respectively in $cm$,are

Similar Questions

If the line $y = 4x + c$ is a tangent to the ellipse $\frac{x^2}{8} + \frac{y^2}{4} = 1$,then $c = \dots$

If the tangents on the ellipse $4x^2 + y^2 = 8$ at the points $(1, 2)$ and $(a, b)$ are perpendicular to each other,then $a^2$ is equal to

Let the equations of two ellipses be $E_1: \frac{x^2}{3} + \frac{y^2}{2} = 1$ and $E_2: \frac{x^2}{16} + \frac{y^2}{b^2} = 1$. If the product of their eccentricities is $\frac{1}{2}$,then the length of the minor axis of ellipse $E_2$ is

The eccentric angle of a point on the ellipse $x^2 + 3y^2 = 6$ at a distance of $2$ units from the centre of the ellipse is:

If the length and breadth of a rectangle of maximum area that can be inscribed in an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are $8 \sqrt{2}$ and $4 \sqrt{2}$ respectively,then the eccentricity of that ellipse is

Vedclass Test Series

Exam Paper Generator

Online Exam Module