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Equation of a...

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Equation of a hyperbola, conjugate hyperbola and pair of their asymptote differs by a constant only.

A

True

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B

False

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Solution

The correct option is A True

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Q. The equation of pair of asymptotes differ from equation of hyperbola and its conjugate by

Q. The equation of asymptotes for a conjugate hyperbola are obtained by multiplying the equations of asymptotes of standard hyperbola by

- 1

The second-degree curve and pair of asymptotes differ by a constant. Let the second-degree curve

S = 0

represent the hyperbola then respective pair of asymptote is given by.

S + λ = 0 (λ \in R)

which represent a pair of straight lines so

λ

can be determined. The equation of asymptotes is

A = s + λ = 0

if equation of conjugate hyperbola of the curve

S = 0

be represents by

S_{1}

A

is arithmetic mean of the curves

S_{1}

S

.

A hyperbola passing through origin has

2 x - y + 3 = 0

x - 2 y + 2 = 0

as its asymptotes, then equation of its transverse and conjugate axes are:

Q. Assertion :The equation of hyperbola whose asymptotes are the lines

3 x - 4 y + 7 = 0

4 x + 3 y + 1 = 0

& which passes through origin is

(3 x - 4 y + 7) (4 x + 3 y + 1) = 7

. Reason: The equation of the pair of asymptotes & hyperbola differ by a constant only.

Q. If the equation to the hyperbola is

3 x^{2} - 5 x y - 2 y^{2} + 5 x + 11 y - 8 = 0

then the equation of conjugate hyperbola and pair of asymptotes is

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