Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
11.6k views
in JEE by (3.3k points)

There are two circles x2+y2=9 and x2+y2-8x-6y+n2=0. n belongs to z. If the two circles have exactly two common tangents, then the number of possible values of n is

1 Answer

+1 vote
by (10.9k points)
selected by
 
Best answer

Eqution of 1st circle x²+y2=9, So it's center is C1​​​​​->(0,0) and radius r1=3 unit.

Equation of 2nd circle

x²+y2-8x-6y+n2=0

=> (x-4)2+(y-3)2-25+n2=0

So it's center C2​​​​​ ->(4,3) and radius r2​​​​​ ->(25-n2)^1/2

C1C2=5

C1C2> |r1-r2|

=>5>(25-n2)^1/2

=> |n| < =4

By the given condition n belongs to Z. The possible values of n should satisfy the relation 25-n2>0 

=> n = -4,-3,-2,-1,0,+1,+2,+3,+4

So number of possible values of n is 9

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...