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Question

# 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
(y3)225(x4)220=1
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B
(x4)225(y3)220=1
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C
(x4)225(y3)215=1
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D
(2x+y11)225(x2y+2)215=1
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Solution

## The correct option is B (x−4)225−(y−3)220=1Here 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

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