Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.
$$
5 y^{2}-9 x^{2}=36
$$

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 hyper bola given to us as life. Life squared minus nine X squared equals two 36. This can be written us dividing the holy question by 36. We get y squared divided by 36 by five minus x squared by four equals to one. Now we know that the standard equation of hi parabola is y squared by is squared minus excess, square by B squared equals to one. So comparing these two equations we have is square equals two 36 x five, which is six, Multiplying the numerator and denominator by. In the root file, This is 605-55. And we have to be square as for which means that B is nothing but two. This is equals two 6' 55. So we have the value of A. And the value of B. Now let's first find out coordinates on the focus which is nothing but zero comma last minus C. Where c squared equals to a square. Let's be square, yes, squares 36 x five. Plus the squares for this comes us Taking the LC. M. This is five 36 plus 20 is 56. To see there's nothing but On the road 56 fine fine. So the coordinate of focus is nothing but zero plus minus Under route 56 months. Right next, let's find the coordinate of the vortices. This is nothing but zero plus minus A. Which is zero comma plus minus six. Route 5 five. Right next let's find eccentricity. He which is see by A. Which is Under route 56 x five divided by six. Route 5 five. This is nothing but under route 56 Divided by Road five divided by six bite Road five Prime Gets canceled. This is under route 56 x six. Now 56 is something about 14 into four, so four route comes out as to this is to Route 146, which is Route 14 three. Next let's find the length of latest rectum, which is to be square by Which is to in to be square is four surrounded by is six divided by Route five. It was in the numerator. This is 455 today.

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