JEE Main 2020 — Circle Question with Solution
From: JEE Main 2020 (Online) 2nd September Morning Slot
Question
The number of integral values of k for which
the line, 3x + 4y = k intersects the circle,
x2 + y2 – 2x – 4y + 4 = 0 at two distinct points is ______.
x2 + y2 – 2x – 4y + 4 = 0 at two distinct points is ______.
Enter your answer
Show full solutionCorrect answer: 0
Correct answer
0
Step-by-step explanation
Circle x2
+ y2
– 2x – 4y + 4 = 0
(x – 1)2 + (y – 2)2 = 1
Centre: (1, 2), radius = 1
Line 3x + 4y – k = 0 intersects the circle at two distinct points.
distance of centre from the line < radius
|11 - k| < 5
6 < k < 5
k {7, 8, 9, ……15} since k I
Total 9 integral value of k.
(x – 1)2 + (y – 2)2 = 1
Centre: (1, 2), radius = 1
Line 3x + 4y – k = 0 intersects the circle at two distinct points.
distance of centre from the line < radius
|11 - k| < 5
6 < k < 5
k {7, 8, 9, ……15} since k I
Total 9 integral value of k.
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Circle chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2020, covering the Circle chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.