1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If the circle x2+y2+8x−4y+c=0 touches the circle x2+y2+2x+4y−11=0 externally and cuts the circle x2+y2−6x+8y+k=0 orthogonally then k=

A
59
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
59
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
19
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
19
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B −59Let s1:x2+y2+8x−4y+c=0∴ centre is 4:(−4,2) and radius =√20−c and s2:x2+y2+2x+4y−11=0centre is C2:(−1,−2) and r2=√5+11=4∵ these two circle one touching each otherc1c2=r1+r2√9+16=√20−c+4⇒5−4=√20−c⇒c=19s3:x2+y2−6x+8y+k=0∴ centre c3:(3,−4)r2=√25−kSince, s1 and s3 cuts orthogonally,r21+r23=(c1c3)2Hence, (20−c)+(25−k)=(√45+36)2⇒k=26−85=−59

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Tangent Circles
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program