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Question

# A line L passing through the focus of the parabola y2=4(x−1), intersects the parabola at two distinct points. If m be the slope of the line L, then

A
mR{0}
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B
1<m<1
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C
m<1 or m>1
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D
None of these
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Solution

## The correct option is A m∈R−{0}The focus of the parabola y2=4(x−1) is (2,0). Any line through the focus is (y−0)=m(x−2),i.e.,y=m(x−2) It will meet the given parabola if m2(x−2)2=4(x−1) or m2x2−4(m2+1)x+4(m2+1)=0 If m≠0, then discriminant =16(m2+1)2−16m2(m2+1) =16(m2+1)>0 ∀ m∈R But if m=0, then x does not have two real and distinct values. ∴m∈R−{0}

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