If m is slope of common tangents y = x2 - x + 1, y = x2 - 3x + 1 then m is
A
16
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B
7
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C
9
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D
None of these
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Solution
The correct option is D None of these Let y = mx + c is common tangent ∴mx+c=x2−x+1⇒x2−(1+4)x+1−c=0mx+c=x2−3x+1x2−(3+m)x+1−c=0 Clearly Δ=0 ⇒(1+4)2−4(1−c)=0⇒m2+2m−3+4c=0⇒(3+m)2−4(1−c)=0⇒m2+6m+5+4c=0 On equality ′m2+4c′ value on both the equations 2m-3=6m+5 ⇒m=−2