Let a circle $C : (x-h)^2 + (y-k)^2 = r^2$, $k > 0$, touch the $x$-axis at $(1, 0)$. If the line $x + y = 0$ intersects the circle $C$ at $P$ and $Q$ such that the length of the chord $PQ$ is 2, then the value of $h + k + r$ is equal to ____.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 24 June 2022, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let a circle

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

k > 0

, touch the

x

-axis at

(1, 0)

. If the line

x + y = 0

intersects the circle

C

P

and

Q

such that the length of the chord

PQ

is 2, then the value of

h + k + r

is equal to ____.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Family of Circles Touching a Line

Same idea in other shifts

Asked 8× in all

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25 Jun 2022, Shift 1 · Q1Let a circle C touch the lines $\mathrm{L_1}$ : $4x-3y+K_1=0$ and $\mathrm{L_2}$ : $4x-3y+K_2=0$ , $K_1, K_2 \in \mathbf{R}$ . If a line…MediumSingle correct
4 Aug 2021, Shift 1 · Q73Consider a family of circles which pass through the point $(1, 1)$ and touch the axis of $y$ . If the centre of such a circle is at…MediumSingle correct
26 Aug 2021, Shift 2 · Q71A circle C touches the line $x=2y$ at the point $(2,\ 1)$ and intersects the circle $C_1:x^2+y^2+2y-5=0$ at two points P and Q such that…HardSingle correct
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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.