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Question

# A line L passing through the focus of the parabola y2=4(xâˆ’1) intersects the parabola in two distinct 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
m R
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D
none of these
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Solution

## The correct option is D none of theseLet the equation of line be y=mx+cSince, it passes through focus (2,0)Then c=−2mSubstitute L in parabola(mx−2m)2=4(x−1)m2x2−4x(m2+1)+4(1+m2)=0Since, it intersection in two distinct points Therefore, b2−4ac=16(1+m2)2−16(1+m2)>0⇒m∈R and m≠0Hence, m∈R−{0}

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