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

If the parabola y=(a−b)x2+(b−c)x+(c−a) touches the x - axis then the line ax + by + c = 0

A
Always passes through a fixed point
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
represents the family of parallel lines
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
always perpendicular to x-axis
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
always has negative slope
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A Always passes through a fixed point
Solving equation of parabola with x-axis ( y=0)

We get (ab)x2+(bc)x+(ca)=0, which should have two equal values of x, as x-axis touches the parabola (bc)24(ab)(ca)=0
(b+c2a)2=02a+b+c=0ax+by+c=0 always passes through (-2, 1) (If we substitute (-2,1) in the equation of the line, then we get -2a+b+c=0, which is true)

flag
Suggest Corrections
thumbs-up
9
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parabola
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon