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Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$$\frac{y^{2}}{9}-\frac{x^{2}}{27}=1$$
Precalculus
Chapter 11
Conic Sections
Section 4
Parabola
Introduction to Conic Sections
Johns Hopkins University
University of Michigan - Ann Arbor
Idaho State University
Lectures
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In mathematics, a continuo…
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in this problem we are given the hyper bolas equation as Y squared by nine minus X squared by 27. Equal store. We know the standard equation of a hyper bola has given us Y squared by white. Square by square minus x square by B squared equal store Comparing these two equations. We get A square is nine which means is three and be squares 27 which means B is Another 27, which is nothing but 32 three. Because we have the value of A and B. Next let's first window coordinate self the fucker. This is nothing but zero comma plus minus seat where she is nothing but underwrote off A squared plus B squared which is nothing but underwrote off nine plus 27 Which comes under all 36 which is six. The coordinates of focus is zero comma less minus six. Next let's find the coordinates of vortices which has given us zero comma plus minus A. Which is zero comma plus minus three. Now, let's find the central city which is nothing but sea over A, which is six divided by three, which is to and length of the latest sector has to be square by A, which is two and two 27 divided by three. This comes as 80. That's.
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