The equation of a tangent to the hyperbola 4x^2 - 5y^2 = 20… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 10 Jan · Shift I

The equation of a tangent to the hyperbola

4x^2 - 5y^2 = 20

parallel to the line

x - y = 2

A.
$x - y - 3 = 0$
B.
$x - y + 9 = 0$
C.
$x - y + 1 = 0$
D.
$x - y + 7 = 0$

Show answer and solution

Correct option: C

Solution

The hyperbola is x²/5 - y²/4 = 1, so a² = 5, b² = 4. For a tangent y = mx + c to this hyperbola, c² = a²m² - b². With slope m = 1 (parallel to x - y = 2), c² = 5(1) - 4 = 1, giving c = ±1. The tangent lines are y = x + 1 and y = x - 1, i.e., x - y + 1 = 0 or x - y - 1 = 0. Among the options, x - y + 1 = 0 is listed, making option 3 correct.

[JEE Main 2019 · 10 Jan · Shift I]

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