wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If C1:x2+y2−20x+64=0 and C2:x2+y2+30x+144=0. The line PQ touches the circle touches C1 at P and C2 at Q. Then the length of the shortest line segment PQ is

A
20
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
15
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
22
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
27
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 20
The equation of the first circle is (x10)2+y2=62
The equation of the second circle is (x+15)2+y2=92
The distance between their centres d is 10(15)=25
If length of traverse common tangent is t1, then d2=(r1+r2)2+t21
t1=252152=20
If length of direct common tangent is t2, then d2=(r2r1)2+t22
t2=25232=616
t1<t2PQmin.=20
220116_117722_ans.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon