wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The pair of straight lines joining the origin to the points of intersection of the line y=22x+c and the circle x2+y2=2 are at right angles, if


A

c2-4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

c2-8

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

c2-9

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

c2-10

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

c2-9


Explanation for the correct option

Given equation of line is,

y=22x+cy-22x=c.......i

Given equation of circle is,

x2+y2=2.......ii

We make i a homogeneous equation by using i

x2+y2-212=0x2+y2-2y-22x2c2=0c2x2+c2y2-2y2-42xy+8x2=0x2c2-16+y2c2-2+82xy=0

The condition for the lines to be perpendicular is

coefficientofx2+coefficientofy2=0c2-16+c2-2=02c2-18=0c2-9=0

Hence, option C is the correct answer.


flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Lines and Points
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon