First slide

Parabola

Question

If $θ$ is the angle between the tangents to the parabola
$y^{2} = 12 x$ passing through the point (–1, 2)
then $| \tan θ |$ is equal to

Moderate

A

2
B

3
C

$\frac{1}{2}$
D

$\frac{2}{3}$

Solution

Equation of any tangent is $y = m x + \frac{3}{m}$ which
passes through (–1, 2) if 2 = $- m + \frac{3}{m}$
$\begin{array}{l} \Rightarrow m^{2} + 2 m - 3 = 0 \\ \Rightarrow m = 1, - 3 \end{array}$
So $| \tan θ | = |\frac{1 + 3}{1 - 3}| = 2$ .

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