The straight line y = 2x + lambda does not me | vedclass

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Question

(B) The given line is $y = 2x + \lambda$ and the parabola is $y^2 = 2x$.Substituting $y = 2x + \lambda$ into the parabola equation: $(2x + \lambda)^2

Vedclass · Accepted Answer

$\lambda > \frac{1}{4}$

Vedclass · Answer

(B) The given line is $y = 2x + \lambda$ and the parabola is $y^2 = 2x$.Substituting $y = 2x + \lambda$ into the parabola equation: $(2x + \lambda)^2 = 2x$.$4x^2 + 4x\lambda + \lambda^2 = 2x$.$4x^2 + (4\lambda - 2)x + \lambda^2 = 0$.For the line not to meet the parabola,the discriminant $D$ must be less than $0$.$D = (4\lambda - 2)^2 - 4(4)(\lambda^2) $16\lambda^2 - 16\lambda + 4 - 16\lambda^2 $-16\lambda + 4 $16\lambda > 4$.$\lambda > \frac{4}{16} = \frac{1}{4}$.

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

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