The equation of the hyperbola whose asymptotes are 3 x -4 y -2-0-2 x - y -1-0 and which passes through the point 1-1 isA- 6 x2-41 x y-44 y2-30 x-2 y-22-0B- 6 x2-11 x y-4 y2 x-2 y-22-0- 6 x2-15 x y-14 y2-6 x-12 y-12-0D- 6 x2-13 x y-6 y2-38 x-37 y-98-0

The correct option is B Equation of pair of asymptotes is (3x + 4y – 2)(2x + y + 1) = 0 ⇒ 6x^2 + 11xy + 4y^2 x + 2y 2 = 0 ∴ Equation of the hyperbola is 6x^ ...

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Standard XII

Mathematics

Conjugate Hyperbola

The equation ...

Question

The equation of the hyperbola whose asymptotes are $3 x + 4 y - 2 = 0, 2 x + y + 1 = 0$ and which passes
through the point (1, 1) is

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Solution

The correct option is B
Equation of pair of asymptotes is $(3 x + 4 y - 2) (2 x + y + 1) = 0 \Rightarrow 6 x^{2} + 11 x y + 4 y^{2} - x + 2 y - 2 = 0$
$∴$ Equation of the hyperbola is $6 x^{2} + 11 x y + 4 y^{2} - x + 2 y + k = 0$
Since it passes through (1, 1) we get, $6 x^{2} + 11 x y + 4 y^{2} - x + 2 y - 22 = 0$

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The equation of the hyperbola whose asymptotes are 3x+4y–2=0,2x+y+1=0 and which passes through the point (1, 1) is

The correct option is B Equation of pair of asymptotes is (3x+4y–2)(2x+y+1)=0⇒6x2+11xy+4y2−x+2y−2=0 ∴ Equation of the hyperbola is 6x2+11xy+4y2−x+2y+k=0 Since it passes through (1, 1) we get, 6x2+11xy+4y2−x+2y−22=0

The equation of the hyperbola whose asymptotes are $3 x + 4 y - 2 = 0, 2 x + y + 1 = 0$ and which passes
through the point (1, 1) is