Question

The latus rectum of the hyperbola 9x2 – 16y2 + 72x – 32y – 16 = 0 is :​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Equation of hyperbola is}$

$\mathsf{9x^2-16y^2+72x-32y-16-0}$

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

$\textsf{Latus rectum of the hyperbola}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{9x^2-16y^2+72x-32y-16-0}$

$\textsf{This can be written as}$

$\mathsf{9(x^2+8x)-16(y^2+2y)=16}$

$\mathsf{9(x^2+8x+16-16)-16(y^2+2y+1-1)=16}$

$\mathsf{9((x+4)^2-16)-16((y+1)^2-1)=16}$

$\mathsf{9(x+4)^2-144-16(y+1)^2+16=16}$

$\mathsf{9(x+4)^2-16(y+1)^2=144}$

$\textsf{Divide bothsides of the equation by 144}$

$\mathsf{\dfrac{(x+4)^2}{16}-\dfrac{(y+1)^2}{9}=144}$

$\mathsf{Comparing\;this\;equation\;with\;\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}$

$\mathsf{Here,\;a^2=16\;\&\;b^2=9}$

$\underline{\mathsf{Length\;of\;latus\;rectum}}$

$\mathsf{=\dfrac{2b^2}{a}}$

$\mathsf{=\dfrac{2{\times}9}{4}}$

$\mathsf{=\dfrac{9}{2}}$

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

Which lines are the directrices of the ellipse?x = −4.25 and x = 8.25

x = −3.25 and x = 9.25

y = −4.25 and y = 8.25

y = −3.25 and y = 9.25

https://brainly.in/question/39034771  

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

then equation of the ellipse is

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