    Question

# If the circle C1:x2+y2=16 intersects another circle C2 of radius 6 in such a manner that their common chord is of maximum length and has slope =12. Then the co-ordinates of the centre of the circle(s) C2 is/are

A
(2,4)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(2,4)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(2,4)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(2,4)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D (2,−4)According to the question, the chord is of maximum possible length ⇒ The diameter of the circle C1:x2+y2=16 is our required common chord . ∵ Slope of the chord is given as 12 ⇒ slope of line perpendicular to the chord would be −2 and its equation would be L:2x+y=c ∵L will pass through both of the centres of the circles. ⇒L:2x+y=0 Let the centre of the circle C2 be Q(h,k) ⇒2h+k=0 ...(1) Now, In ΔPAQ 62=42+AQ2and AQ2=h2+k2⇒h2+k2=20 ..(2) Using (1) and (2) we get : h=±2⇒k=∓4 ∴ The co-ordinates of the circle C2 are (2,−4) and (−2,4).  Suggest Corrections  0      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   MATHEMATICS
Watch in App  Explore more
Join BYJU'S Learning Program
Select...