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Question

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

A
1<m<1
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B
m<1 or m>1
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C
mϵR
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D
None of the above
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Solution

The correct option is D None of the above
Let y=Y,x1=X
Then, the equation becomes Y2=4X.
So, the focus =(2,0)
Any line through the focus is y=m(x2)
On solving this with y24(x10
m2(x2)2=4(x1)
m2x24(m2+1)x+4(m2+1)=0
If m0,D=16(m2+1)216m2(m2+1)
=16(m2+1)>0, for all m
But, if m=0, then x does not have two real distinct values.
So, mϵR except m=0
mϵR{0}.

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