JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let a line L pass through the point of intersection of the lines

bx + 10y - 8 = 0

and

2x - 3y = 0

b \in \mathbf{R} - \left\{\frac{4}{3}\right\}

. If the line L also passes through the point

(1, 1)

and touches the circle

17(x^2 + y^2) = 16

, then the eccentricity of the ellipse

\frac{x^2}{5} + \frac{y^2}{b^2} = 1

is :

(1) $\frac{2}{\sqrt{5}}$
(2) $\sqrt{\frac{3}{5}}$ Official answer
(3) $\frac{1}{\sqrt{5}}$
(4) $\sqrt{\frac{2}{5}}$

Official answer

Option 2

NTA final key.

Chapter: Straight Lines
Topic: Circle Tangents
Idea tested: Condition of tangency

Same idea in other shifts

Asked 11× in all

5 Apr 2024, Shift 2 · Q14Let $ABCD$ and $AEFG$ be squares of side 4 and 2 units, respectively. The point $E$ is on the line segment $AB$ and the point $F$ is on…MediumSingle correct
1 Feb 2024, Shift 1 · Q29Let the line $L:\sqrt{2}x+y=\alpha$ pass through the point of the intersection P (in the first quadrant) of the circle $x^2+y^2=3$ and the…HardNumerical value
29 Jan 2024, Shift 1 · Q27Equations of two diameters of a circle are $2x-3y=5$ and $3x-4y=7$ . The line joining the points $\left(-\frac{22}{7},-4\right)$ and…MediumNumerical value
30 Jun 2022, Shift 1 · Q14Consider three circles : $C_1 : x^2 + y^2 = r^2$ $C_2 : (x-1)^2 + (y-1)^2 = r^2$ $C_3 : (x-2)^2 + (y-1)^2 = r^2$ If a line L :…HardSingle correct
31 Aug 2021, Shift 1 · Q86If the variable line $3x+4y=\alpha$ lies between the two circles $(x-1)^2+(y-1)^2=1$ and $(x-9)^2+(y-1)^2=4$ , without intercepting a chord…HardNumerical value
8 Jan 2020, Shift 2 · Q64If a line, $y = mx + \mathrm{c}$ is a tangent to the circle, $(x - 3)^2 + y^2 = 1$ and it is perpendicular to a line $\mathrm{L}_1$ , where…MediumSingle correct
9 Jan 2020, Shift 1 · Q65A circle touches the $y$ -axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to…MediumSingle correct
2 Sep 2020, Shift 1 · Q74The number of integral values of k for which the line, $3x+4y=k$ intersects the circle, $x^{2}+y^{2}-2x-4y+4=0$ at two distinct points is…MediumNumerical value

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.