MHT CET2009MathematicsHyperbola

Focus of hyperbola is ( 3,0) and equation of tangent is 2 x+y-4=0 , find the equation of hyperbola.

Options

A4 x²-5 y²=20
B5 x²-4 y²=20
C4 x²-5 y²=1
D5 x²-4 y²=1

Correct answer

A. 4 x²-5 y²=20

Step-by-step solution

Given, aligned ( a e, 0) &=( 3,0) a e &=3 & a² e² &=9 & b²+a² &=9 & 2 x+y-4 &=0 & y=& 2 x+4 aligned is the tangent to the hyperbola. (4)²=a²(-2)²-b² 4 a²-b²=16 On solving Eqs. (i) and (ii), we get a²=5, b²=4 Equation of hyperbola is x² 5 - y² 4 =1 4 x²-5 y²=20

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