Question

The eccentricity of the ellipse represented by x = 5 (cos t + sin t), y = 3 (cos t – sin t) where t is parameter, is given by e, then 20e is equal to

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Ellipse is}$

$\mathsf{x=5(cost+sint)}$

$\mathsf{y=3(cost-sint)}$

$\underline{\textsf{To find:}}$

$\textsf{The value of 20e}$

$\underline{\textsf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{x=5(cost+sint)}$

$\mathsf{\dfrac{x}{5}=cost+sint}$....(1)

$\mathsf{y=3(cost-sint)}$

$\mathsf{\dfrac{y}{3}=cost-sint}$....(2)

$\mathsf{Squaring\;and\;adding\;(1)\;and\;(2)}$

$\mathsf{\dfrac{x^2}{25}+\dfrac{y^2}{9}=(cost+sint)^2+(cost-sint)^2}$

$\mathsf{\dfrac{x^2}{25}+\dfrac{y^2}{0}=(cos^2t+sin^2t+2\,sint\,cost)+(cos^2t+sin^2t-2\,sint\,cost)}$

$\mathsf{\dfrac{x^2}{25}+\dfrac{y^2}{9}=2}$

$\implies\mathsf{\dfrac{x^2}{50}+\dfrac{y^2}{18}=1}$

$\mathsf{Comparing\;this\;with\;standard\;form\;of\;ellipse\;\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\;we\;get}$

$\mathsf{a^2=50\;\;\&\;\;b^2=18}$

$\mathsf{Then,}$

$\mathsf{Eccentricity,\;e=\sqrt{1-\dfrac{b^2}{a^2}}}$

$\mathsf{Eccentricity,\;e=\sqrt{1-\dfrac{18}{50}}}$

$\mathsf{Eccentricity,\;e=\sqrt{\dfrac{32}{50}}}$

$\mathsf{Eccentricity,\;e=\sqrt{\dfrac{16}{25}}}$

$\mathsf{Eccentricity,\;e=\dfrac{4}{5}}$

$\mathsf{20\,e=20{\times}\dfrac{4}{5}=4{\times}4=16}$

$\underline{\textsf{Answer:}}$

$\bf\,The\,value\,of\,20\,e\;is\;16$

$\underline{\textsf{Find more:}}$

LIf vertices are (2,-2), (2, 4) and e =1/3

then equation of the ellipse is

​https://brainly.in/question/19651956

The eccentricity of an ellipse with its centre at the origin is 1/2.if one of the directrix is x=4,then equation of ellipse is

https://brainly.in/question/1373399

Answer 2

Step-by-step explanation:

$\huge\bold{\underline{\underline{\red{Global\:warming}}}}$

Climate change includes both the global warming driven by human emissions of greenhouse gases, and the resulting large-scale shifts in weather patterns