0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

# CirclesNumber of common tangentsI:x2+y2=4x2+y2−8x+12=0a) 0II:x2+y2=1x2+y2−2x−6y+6=0b) 1III:x2+y2=16x2+y2−8x+6y−56=0c) 4IV: x2+y2−2x−6y+9=0x2+y2+6x−2y+1=0d)3

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

## The correct option is A d,c,b,cI. S1:x2+y2=4 and S2:x2+y2−8x+12=0 C1≡(0,0) C2≡(4,0) r1=2 r2=2S1 and S2 Touch each other externally, So no of common tangent are 3.II. S1:x2+y2=1 and S2:x2+y2−2x−6y+6=0 C1≡(0,0) C2≡(1,3) r1=1 r2=2C1C2=√10 and r1+r2=3C1C2>r1+r2S1 & S2 does not intersect each other. So no of common tangents are 4.III. S1:x2+y2=16 and S2:x2+y2−8x+6y+56=0 C1≡(0,0) C2≡(4,3) r1=4 r2=9C1C2=5 and r1+r2=13r2−r1=5C1C2=r2−r1S1 and S2 Touches internally so no of common tangent are 1.IV. x2+y2−2x−6x+9=0 C1≡(1,3) r1=1x2+y2+6x−2y+1=0C2≡(−3,1)r2=3C1C2>r1r2S1 and S2 are not intersection so, no of common tangent is 4.So, d,c,b,c

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Line and Ellipse
MATHEMATICS
Watch in App
Join BYJU'S Learning Program