Question

The equation of a tangent to the hyperbola
4x^2 - 5y^2 = 20 parallel to the line x - y = 2 is

(a) x - y - 3 = 0
(b) x - y + 9 = 0
(c) x - y + 1 = 0
(d) x - y + 7 = 0​

Answer 1

Given equation hyperbola is

$\frac{ {x}^{2} }{5} - \frac{ {y}^{2} }{4} = 1$

Now, equation of the tangent to the hyperbola is

$y = mx ± \: \sqrt{ {a}^{2} {m}^{2} - {b}^{2} }$

....(i)

Since, the tangent is parallel to X - Y = 2

∴ slope of the tangent is 1

∴ (i) becomes

$y = mx ± \: \sqrt{ 5 - 4 }$

=> y = x + 1 or y = x - 1

=> x - y + 1 = 0 or x - y - 1 = 0

Option (c) is correct !!

Answer 2

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