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10-2. Parabola, Ellipse, Hyperbola
hard
अतिपरवलय $4 x ^{2}-5 y ^{2}=20$ की एक स्पर्श रेखा जो रेखा $x - y =2$ के समांतर है, का समीकरण है
A
$x -y + 1 = 0$
B
$x -y + 7 = 0$
C
$x -y + 9 = 0$
D
$x -y -3 = 0$
(JEE MAIN-2019)
Solution
Hyperbola is $\frac{{{x^2}}}{5} – \frac{{{y^2}}}{4} = 1$
Equation of its tangent in slop from is $y = mx \pm \sqrt {5{m^2} – 4} $
Hence tangent with slope $1$ is $y = x \pm 1$
Standard 11
Mathematics
