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

If a tangent to the circle x2+y2=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:

A
x2+y22xy=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x2+y22x2y2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2+y24x2y2=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x2+y216x2y2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C x2+y24x2y2=0
Let mid-point of PQ be S having coordinates (h,k).
Hence, coordinates of P and Q are (2h,0) and (0,2k) respectively.
Also, the equation of PQ using Intercept form is
x2h+y2k=1
Given circle is x2+y2=1
C=(0,0),r=1
Also, PQ is tangent to circle, so distance from centre to PQ is equal to radius
∣ ∣ ∣ ∣ ∣ ∣1(12h)2+(12k)2∣ ∣ ∣ ∣ ∣ ∣=114h2+14k2=1k2+h2=4h2k2

Hence, the locus is
x2+y24x2y2=0

flag
Suggest Corrections
thumbs-up
28
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon