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

If two distinct chords, drawn from the point(p, q) on the circle x2+y2=px+qy(where pq≠0) are bisected by the x-axis, then

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

The correct option is D >

Let PQ be a chord of the given circle passing through P(p, q) and the coordinates of Q be (x, y)
Since PQ is bisected by the x-axis, the mid-point of PQ lies on the x axis which gives y = - q
Now Q lies on the circle x2+y2pxqy=0
x2+q2px+q2=0x2px+2q2=0(i)
which gives two values of x and hence the coordinates of two points Q and R (say), so that the chords PQ and PR are bisected by x-axis. If the chords PQ and PR are distinct, the roots of (i) are real distinct.
the discriminant p28q2>0 p2>8q2

flag
Suggest Corrections
thumbs-up
15
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Tango With Straight Lines !!
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon