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`

Find the coordinates of the foci and the vertices, the eccentricity an

1.	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» Given equation is, `49y^2-16x^2 = 784` We will convert this equation into standard form. `=>49/784y^2-16/784x^2 = 1` `=> y^2/16-x^2/49 =1 ` So, this is our standard equation of hyperbola with, `a = 4, b = 7` `c = sqrt(a^2+b^2) = sqrt(16+49) = sqrt65` Here, as `y^2` is positive, major-axis will be `Y-`axis. Now, foci will be `(0,+-c) = (0,+-sqrt65).` Vertices will be `(0,+-a) = (0,+-4).` Eccentricity `= c/a = sqrt65/4.` Length of latus rectum ` = 2b^2/a = 2**49/4 = 49/2.`

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