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

A line L passing through the focus of the parabola y2=4(x1), intersects the parabola at two distinct points. If m be the slope of the line L, then

A
mR{0}
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
1<m<1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
m<1 or m>1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A mR{0}
The focus of the parabola y2=4(x1) is (2,0).
Any line through the focus is
(y0)=m(x2),i.e.,y=m(x2)
It will meet the given parabola if
m2(x2)2=4(x1)
or m2x24(m2+1)x+4(m2+1)=0
If m0, then
discriminant =16(m2+1)216m2(m2+1)
=16(m2+1)>0 mR
But if m=0, then x does not have two real and distinct values.
mR{0}

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon