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Question

# A line L passing through the focus of the parabola y2=4(xâˆ’1), intersects the parabola in two distinet points. If â€²mâ€² be the slope of the line â€²Lâ€² 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 aboveLet y=Y,x−1=XThen, the equation becomes Y2=4X.So, the focus =(2,0)Any line through the focus is y=m(x−2)On solving this with y2−4(x−10m2(x−2)2=4(x−1)⇒m2x2−4(m2+1)x+4(m2+1)=0If m≠0,D=16(m2+1)2−16m2(m2+1)=16(m2+1)>0, for all mBut, if m=0, then x does not have two real distinct values.So, mϵR except m=0∴mϵR−{0}.

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