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If `y + b = m_(1)(x + a)` and `y + b = m_(2)(x+a)` are two tangents to the parabola `y^(2) =4ax`, then

A

`m_(1)+m_(2)=0`

B

`m_(1)m_(2)=1`

C

`m_(1)m_(2)=-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, two given pass through (-a, -b) which is a point on the directrix of the parabola `y^(2)=4ax`. So the angle between the tangents is `pi//2`.
Hence, `m_(1)m_(2)=-1`.
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