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10-2. Parabola, Ellipse, Hyperbola
normal
Equation of hyperbola with asymptotes $3x - 4y + 7 = 0$ and $4x + 3y + 1 = 0$ and which passes through origin is
A
$12x^2 - 7xy - 1 2y^2 + 17x - 31y = 0$
B
$12x^2 - 7xy + 12y^2 + 31x + 17y = 0$
C
$12x^2 - 7xy - 12y^2 + 31x + 17y = 0$
D
$12x^2 - 7xy - 12y^2 - 31x - 17y = 0$
Solution
Joint equation of asymptotoes
$(3 x-4 y+7)(4 x+3 y+1)=0$
$\therefore$ Equation hyperbola and joint equation of asymptotes differ by a constant
$\therefore(3 x-4 y+7)(4 x+3 y+1)+\lambda=0$
(Equaiton of hperbola)
$\therefore$ Passes through $(0,0)=(7)(1)+k=0$
$\Rightarrow \mathrm{k}=-7$
$\therefore$ Euqation $(3 x-4 y+7) \cdot(4 x+3 y+1)-7=0$
$=12 x^{2}-7 x y-12 y^{2}+31 x+17 y=0$
Standard 11
Mathematics
