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+y2âˆ’pxâˆ’qy=0 (where pqâ‰ 0) are bisected by the x-axis, then

A
p2=q2
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
p2=8q2
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
p2<8q2
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
p2>8q2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D p2>8q2Let B(h, 0) be the midpoint of the chord drawn from point A(p, q). Also, the center of the circle is C(p2,q2). Then, we have BC⊥AB. Therefore, (q2)−0(p2)−h(q−0p−h)=−1 ...(Product of slopes of two perpendicular lines, m1.m2=−1)∴(qp−2h)(q−0p−h)=−1∴2h2−3ph+p2+q2=0 Since two such chords exist, the above equation must have two distinct real roots, i.e., Discriminant > 0 ∴9p2−8(p2+q2)>0or p2>8q2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Definition and Standard Forms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program