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Subtangent

If y + 3 = ...

Question

If y + 3 = $m_{1}$ (x + 2) and y + 3 = $m_{2}$ (x + 2) are two tangents to the parabola $y^{2}$ = $8 x$ , then

A

m_{1}

+

m_{2}

= 0

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B

m_{1} m_{2}

= 1

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C

m_{1} m_{2}

= -1

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D

None of these

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Solution

The correct option is C $m_{1} m_{2}$ = -1
condition for tangency is

$c = \frac{a}{m}$

So for first case

$2 m_{1} - 3 = \frac{2}{m_{1}}$ and

$2 m_{2} - 3 = \frac{2}{m_{2}}$

Subtracting,

$2 (m_{1} - m_{2}) = \frac{2}{m_{1}} - \frac{2}{m_{2}}$

$2 (m_{1} - m_{2}) = \frac{2 (m_{2} - m_{1})}{m_{1} m_{2}}$

$2 (m_{1} - m_{2}) = - \frac{2 (m_{1} - m_{2})}{m_{1} m_{2}}$

$m_{1} m_{2} = - 1$

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