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

# Two chords are drawn from the point P(h,k) on the circles x2+y2−hx−ky=0. If the y-axis divides both the chords in the ratio 1:3, then which of the following is/are correct?

A
9k2>16h2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
k2>48h2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
9k216h2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4k2=h2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct options are A 9k2>16h2 B k2>48h2 Case-1: Ratio =1:3 (0,a)=(h+3x14,k+3y14) ⇒0=h+3x14, a=k+3y14 ⇒x1=−h3, y1=4a−k3 Since, (x1,y1) lies on the circle. ⇒x21+y21−hx1−ky1=0 ⇒h29+(4a−k)29+h23+k2−4ak3=0 ⇒4a2−5ak+(h2+k2)=0 Now, D>0 for two different chords. 25k2−16(h2+k2)>0 ⇒9k2>16h2 Case-2: Ratio =3:1 (0,a)=(3h+x14,3k+y14) ⇒0=3h+x14, a=3k+y14 ⇒x1=−3h, y1=4a−3k ⇒9h2+(4a−3k)2+3h2+3k2−4ak=0 ⇒4a2−7ak+3(h2+k2)=0 Now, D>0 for two different chords. 49k2−48(h2+k2)>0 ⇒k2>48h2

Suggest Corrections
3
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Join BYJU'S Learning Program