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Question: If y+b = m<sub>1</sub>(x+a) and y+b = m<sub>2</sub>(x+a) are two tangents to the parabola y<sup>2</s...

If y+b = m1(x+a) and y+b = m2(x+a) are two tangents to the parabola y2 = 4ax, then

A

m1 + m2 = 0

B

m1m2 = 1

C

m1m2 = -1

D

None of these

Answer

m1m2 = -1

Explanation

Solution

The given lines are passes through (-a, -b), this is a point on the directrix x = -a. The tangents drawn from any point on the directrix to the parabola are at right angles.∴ m1m2 = -1