Question
Question: The slopes of two tangents drawn from (1, 4) to the parabola y<sup>2</sup> = 12x are...
The slopes of two tangents drawn from (1, 4) to the parabola y2 = 12x are
A
1, 4
B
1, 3
C
1, 2
D
2, 3
Answer
1, 3
Explanation
Solution
The slopes of the tangents to the parabola y2 = 4ax passing through (x1, y1) are given by the equation
m2x1 – my1 + a = 0
Given (x1,y1) = (1, 4), a = 3.
∴ Slopes are given by m2.1 – m.4 + 3 =0
m2 – 4m+3 = 0
⇒ m = 1, 3.