JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let

x^2+y^2+Ax+By+C=0

be a circle passing through

(0, 6)

and touching the parabola

y=x^2

(2, 4)

. Then

A+C

is equal to ______.

(1)16Official answer
(2) $88/5$
(3)72
(4) $-8$

Official answer

Option 1

NTA final key (2022 Session 1).

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Common Tangent to Circle and Conic

Same topic in other shifts

All Circle Tangents questions

6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the $x$ -axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines…HardNumerical value
7 Apr 2025, Shift 1 · Q12Let $C_1$ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $C_2$ be the circle with centre $(1, 3)$ …MediumSingle correct
8 Apr 2024, Shift 1 · Q15Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at…MediumSingle correct
9 Apr 2024, Shift 1 · Q29Let the centre of a circle, passing through the points $(0,0)$ , $(1,0)$ and touching the circle $x^2+y^2=9$ , be $(h,k)$ . Then for all…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

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.