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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.`(x^2)/(16)-(y^2)/9=1`

Text Solution

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`(x^(2))/(16)-(y^(2))/(9)=1`
Here, `a^(2)=16,b^(2)=9rArra=4,b=3`
`:."Vertices"-=(pma,0)-=(pm4,0)`
Eccentricity `e=sqrt(1+(b^(2))/(a^(2)))=sqrt(1+(9)/(16))=(5)/(4)`
Coordinates of foci `-=(pmae,0)-=(pm5,0)`
Latus rectum `=(2b^(2))/(a)=(2xx9)/(4)=(9)/(2)`
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