JEE PYQ: Hyperbola Question 18
Question 18 - 2019 (10 Jan Shift 1)
The equation of a tangent to the hyperbola $4x^2 - 5y^2 = 20$ parallel to the line $x - y = 2$ is:
(1) $x - y + 1 = 0$
(2) $x - y + 7 = 0$
(3) $x - y + 9 = 0$
(4) $x - y - 3 = 0$
Show Answer
Answer: (1)
Solution
Hyperbola: $\frac{x^2}{5} - \frac{y^2}{4} = 1$, $a^2 = 5$, $b^2 = 4$. Slope $m = 1$. Tangent: $y = x \pm \sqrt{5 \cdot 1 - 4} = x \pm 1$. So $x - y + 1 = 0$ or $x - y - 1 = 0$. Answer: $x - y + 1 = 0$.
BETA
