If the length of latus rectum of a hyperbola whose eccentricity is 3√5, centre (4,3) and axis is parallel to coordinate axis is 8 units, then the equation(s) of the hyperbola is/are
A
(y−3)225−(x−4)220=1
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B
(x−4)225−(y−3)220=1
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C
(x−4)225−(y−3)215=1
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D
(2x+y−11)225−(x−2y+2)215=1
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Solution
The correct option is B(x−4)225−(y−3)220=1 Here 2b2a=8 and 3√5=√1+b2a2 ⇒45=b2a2 ⇒a=5,b=2√5
Thus the equations of the given hyperbola is, if transverse axis parallel to x-axis and conjugate axis parallel to y-axis: (x−4)225−(y−3)220=1
The equation of hyperbola if transverse axis is parallel to y-axis and conjugate axis parallel to x-axis is: (y−3)225−(x−4)220=1