JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q30

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

Let the lines

y+2x=\sqrt{11}+7\sqrt{7}

and

2y+x=2\sqrt{11}+6\sqrt{7}

be normal to a circle

C:(x-h)^2+(y-k)^2=r^2

. If the line

\sqrt{11}y-3x=\frac{5\sqrt{77}}{3}+11

is tangent to the circle

C

, then the value of

(5h-8k)^2+5r^2

is equal to __________.

Official answer

816

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Normal Passes Through Center

Same idea in other shifts

Asked 4× in all

13 Apr 2023, Shift 2 · Q13Let the centre of a circle C be $(\alpha,\beta)$ and its radius $r<8$ . Let $3x+4y=24$ and $3x-4y=32$ be two tangents and $4x+3y=1$ be a…MediumSingle correct
25 Feb 2021, Shift 1 · Q62Let the lines $(2-i)z = (2+i)\bar{z}$ and $(2+i)z + (i-2)\bar{z} - 4i = 0$ , (here $i^2 = -1$ ) be normal to a circle C. If the line…HardSingle correct
17 Mar 2021, Shift 1 · Q74The line $2x-y+1=0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x-2y=4$ . Then, the radius of…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.