JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

If two tangents drawn from a point

(\alpha, \beta)

lying on the ellipse

25x^2+4y^2=1

to the parabola

y^2=4x

are such that the slope of one tangent is four times the other, then the value of

(10\alpha+5)^2+(16\beta^2+50)^2

equals ______.

Official answer

2929

NTA final key (2022 Session 1).

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Condition for Line to be Tangent

Same idea in other shifts

Asked 5× in all

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25 Jul 2022, Shift 1 · Q28Let the equation of two diameters of a circle $x^2+y^2-2x+2fy+1=0$ be $2px-y=1$ and $2x+py=4p$ . Then the slope $m\in(0,\infty)$ of the…MediumNumerical value
28 Jul 2022, Shift 1 · Q27For the hyperbola $H:x^2-y^2=1$ and the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b>0$ , let the (1) eccentricity of E be reciprocal…HardNumerical value
24 Jun 2022, Shift 1 · Q15Let $\lambda x-2y=\mu$ be a tangent to the hyperbola $a^2x^2-y^2=b^2$ . Then…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 42 of the 174 JEE Main shifts held from 2017 to 2026.