The equation to the locus of the midpoints of chords of the circle x2+y2=r2 having a constant length 2l is
A
x2+y2=l2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x2+y2=r2−l2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
x2+y2=r2+l2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x2+y2=4l2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Bx2+y2=r2−l2
Let P(x1,y1) be a point on the locus
Then P is the mid point of a chord AB of the circle x2+y2=r2
Now OP2+AP2=OA2⇒x21+y21=r2−l2 ∴ThelocusofPisx2+y2=r2−l2