Question
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