JEE Main 2019 — Circle Question with Solution
From: JEE Main 2019 (Online) 9th January Evening Slot
Question
If the circles
x2 + y2 16x 20y + 164 = r2
and (x 4)2 + (y 7)2 = 36
intersect at two distinct points, then :
x2 + y2 16x 20y + 164 = r2
and (x 4)2 + (y 7)2 = 36
intersect at two distinct points, then :
Choose an option
Show full solutionCorrect option: D
Correct answer
D1 < r < 11
Step-by-step explanation
Circles are x2 + y2 16x 20y + 164 = r2 c1 (8, 10)
and (x 4)2 + (y 7)2 = 36
they intersect at two distinct points
Now
from (i) and (ii)
r (1, 11)
and (x 4)2 + (y 7)2 = 36
they intersect at two distinct points
Now
from (i) and (ii)
r (1, 11)
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 2019, 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.