JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q66

Question 66 of 75 in this shift, Maths question 16 of 25.

Let P(3, 3) be a point on the hyperbola,

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

. If the normal to it at P intersects the

x

-axis at (9, 0) and e is its eccentricity, then the ordered pair

(a^2, e^2)

is equal to :

(1) $\left(\frac{9}{2}, 2\right)$
(2) $(9, 3)$
(3) $\left(\frac{3}{2}, 2\right)$
(4) $\left(\frac{9}{2}, 3\right)$ Official answer

Official answer

Option 4

NTA final key (Sep 2020).

Chapter: Conic Sections
Topic: Normals to Conics
Idea tested: Hyperbola Normal Point Form

Same idea in other shifts

Asked 6× in all

11 Apr 2023, Shift 2 · Q27Let the tangent to the parabola $y^2 = 12x$ at the point $(3, \alpha)$ be perpendicular to the line $2x + 2y = 3$ . Then the square of…HardNumerical value
26 Jul 2022, Shift 1 · Q13Let the tangent drawn to the parabola $y^2 = 24x$ at the point $(\alpha,\ \beta)$ is perpendicular to the line $2x + 2y = 5$ . Then the…MediumSingle correct
25 Jun 2022, Shift 2 · Q29Let the eccentricity of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be $\frac{5}{4}$ . If the equation of the normal at the point…HardNumerical value
26 Jun 2022, Shift 2 · Q13The normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$ at the point $(8, 3\sqrt{3})$ on it passes through the point :MediumSingle correct
8 Jan 2020, Shift 2 · Q65If a hyperbola passes through the point $\mathrm{P}(10, 16)$ and it has vertices at $(\pm 6, 0)$ , then the equation of the normal to it at…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.