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Maths-

General

Easy

Question

The straight line y = 2x + $lambda$ does not meet the parabola y² = 2x, if

$λ$   < $\frac{1}{4}$
$λ$   > $\frac{1}{4}$
$λ$ = 4
$λ$   = 1

The correct answer is: $lambda$ > $fraction numerator 1 over denominator 4 end fraction$

line y = 2x + $lambda$ …(i)
Parabola y² = 2x …(ii)
From (i) & (ii) (2x+ $lambda$ )² = 2x
$rightwards double arrow$ 4x² + 4x $lambda$ + $lambda$ ² = 2x
$rightwards double arrow$ 4x² + 2x(2 $lambda$ – 1) + $lambda$ ² = 0
Does not meet the parabola D < 0
$rightwards double arrow$ 4(2 $lambda$ – 1)² – 4(4)( $lambda$ ²) < 0
$rightwards double arrow$ 4[4 $lambda$ ² + 1 – 4 $lambda$ – 4 $lambda$ ²] < 0
$rightwards double arrow$ 1 – 4 $lambda$ < 0 $rightwards double arrow$ $lambda$ > ¼

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