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Question: The line lx + my + n = 0 will touch the parabola y<sup>2</sup> = 4ax, if...

The line lx + my + n = 0 will touch the parabola y2 = 4ax, if

A

mn = al2

B

lm = an2

C

ln = am2

D

mn = al

Answer

ln = am2

Explanation

Solution

ln + my + n = 0 ̃ y = lxmnm\frac{\mathcal{- l}x}{m} - \frac{n}{m}

Condition of tangency c = am\frac{a}{m} ̃ nm=al/m\frac{- n}{m} = \frac{a}{\mathcal{- l}/m}

̃ nm=aml\frac{- n}{m} = \frac{am}{\mathcal{- l}} ̃ nl = am2