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
0 votes
1.0k views
in Co-ordinate geometry by (30 points)
edited by

The minimum distance between the circle \( x^{2}+y^{2}=9 \) and the curve \( 2 x^{2}+10 y^{2}+6 x y=1 \) is 

1) \( 2 \sqrt{2} \) 

2) 2 

3) \( 3-\sqrt{2} \) 

4) \( 3-\frac{1}{\sqrt{11}} \)

Please log in or register to answer this question.

1 Answer

0 votes
by (45.0k points)

Correct option is 2) 2

x2 + y2 = 9....(i)

centre of circle is (0,0)

2x2 + 10y2 + 6xy = 1....(ii)

Partial differentiate with respect to x

4x + 6y = 0

Partial differentiate with respect to y

20y + 6x = 0

Solution of above given (x,y) = (0,0)

Hence centre of (ii) is also (0,0)

Also shortest distance is always found along common normal, and normal of circle passes through centre (0,0), hence we need shortest distance of origin from any point (x,y) on (ii) is

Now you to minimize x2 + y2 subjected to condition 

2x2 + 10y2 + 6xy = 1 which will given d = 1

Hence

Shortest distance = Radius −d = 3 − 1 = 2

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.

...