Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.
$$
49 y^{2}-16 x^{2}=784
$$

Answer

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Precalculus

NCERT Class 11 - Math

Chapter 11

Conic Sections

Section 4

Parabola

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Video Transcript

in this problem we have the equation of hyperbole. Um Given to us as 49, Y Square minus 16 X squared equals two 17. Let us divide the whole equation by 74. This becomes wide square by 16 xs squared by 49 equals to one. Now we know that the standard equation of a hip Ebola is why square by square minus X squared by a b squared equals to one. Comparing these two equations. We get a 16 which means is four. The square is 49 which means we is seven. Now let's first find the coordinates of the focus which is nothing but zero comma plus minus seat where she is on the route of a squared plus B square. This is a little of 16 plus 49. This is a little dark 65. So the focus is at zero comma plus minus good 65. Next let's find the coordinates of the what is this? Which is nothing but zero plus minus A. Which is zero comma plus minus four. Next is the eccentricity E, which is C by A. Which is Route 65 5 fold, and finally the length of Lake District. Um Just to be square by A. Which is two and two 49 divided by full. Just 49. That's all.

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