Planet M orbits around its sun,S,in an ellipt | vedclass

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

Question

(A) Let the major axis be along the $y$-axis. The distance between the closest point $M_1$ and farthest point $M_2$ is the length of the major axis $2

Vedclass · Accepted Answer

$\frac{x^2}{36} + \frac{(y+8)^2}{100} = 1$

Vedclass · Answer

(A) Let the major axis be along the $y$-axis. The distance between the closest point $M_1$ and farthest point $M_2$ is the length of the major axis $2b = 18 + 2 = 20$,so $b = 10$.Given the sun $S$ is at $(0, 0)$ and is a focus,the distance from the center $(0, -k)$ to the focus is $be = 8$. Since the focus $S$ is at $(0, 0)$ and the other focus is on the negative $y$-axis,the center must be at $(0, -8)$.Thus,$b = 10$ and $be = 8$,which implies $e = 0.8$.Using $a^2 = b^2(1 - e^2)$,we get $a^2 = 100(1 - 0.64) = 100(0.36) = 36$,so $a = 6$.The equation of the ellipse with center $(0, -8)$ and major axis along the $y$-axis is $\frac{x^2}{a^2} + \frac{(y - (-8))^2}{b^2} = 1$,which simplifies to $\frac{x^2}{36} + \frac{(y+8)^2}{100} = 1$.

Similar Questions

In which of the following reactions does the hybridisation of the central atom change from $sp^2$ to $sp^3$?

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\vec B$ exists parallel to the axis of rotation. The $e.m.f.$ induced between two ends of the rod is

Which of the following plants is primarily cultivated for the extraction of oil?

The presence of diversity at the junction of territories of two different habitats is known as

Which of the following pairs will not produce dihydrogen gas?

Vedclass Test Series

Exam Paper Generator

Online Exam Module