If lx + my + n = 0 is tangent to the parabola | vedclass

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Question

(D) Given the line $lx + my + n = 0$ $(i)$ and the parabola $x^2 = y$ $(ii)$.To find the intersection,substitute $y = x^2$ into the line equation: $lx

Vedclass · Accepted Answer

$l^2 = 4mn$

Vedclass · Answer

(D) Given the line $lx + my + n = 0$ $(i)$ and the parabola $x^2 = y$ $(ii)$.To find the intersection,substitute $y = x^2$ into the line equation: $lx + m(x^2) + n = 0$.Rearranging gives the quadratic equation: $mx^2 + lx + n = 0$.Since the line is tangent to the parabola,the discriminant of this quadratic equation must be zero $(D = 0)$.$D = b^2 - 4ac = l^2 - 4(m)(n) = 0$.Therefore,the condition of tangency is $l^2 = 4mn$.

If $lx + my + n = 0$ is tangent to the parabola $x^2 = y$,then the condition of tangency is

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