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
m∈R−{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 Am∈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}