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

Find the values of non-negative real numbers h1,h2,h3,k1,k2,k3 such that the algebraic sum of the perpendiculars drawn from points (2,k1),(3,k2),(7,k3),(h1,4),(h2,5),(h3,3) on a variable line passing through (2,1) is zero.

A
h1=h2=h3=k1=k2=k3=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
h1=h2=h3=k1=k2=k3=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
h1=h2=h3=k1=k2=k3=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
h1=h2=h3=k1=k2=k3=4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B h1=h2=h3=k1=k2=k3=0
Distance of point (h.k) from line lx+my+n=0 is
lh+mk+nl2+m2
Let ax+by+c=0 be the variable line
Passes through (2,1)2a+b+c=0
Now,
According to question,
2a+k1b+ca2+b2+3a+k2b+ca2+b2+7a+k3b+ca2+b2+h1a+4b+ca2+b2+h2a+5b+ca2+b2+h3a3b+ca2+b2=0
a[2+3+7+h1+h2+h3]+b[k1+k2+k3+4+53]+6c=0
a[12+h1+h2+h3]+b[6+k1+k2+k3]+6c=0
a[2+h1+h2+h3]6+b[1+k1+k2+k3]6+c=0
Comparing with 2a+b+c=0
h1+h2+h3=0 & k1+k2+k3=0
h1,h2,h3,k1,k2 & k3 are non negative
h1=h2=h3=k1=k2=k3=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Line and a Point, Revisited
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon