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Q)

The angle between the two tangents drawn from the point $(-4 , 4)$ to $y^{2}=16x $ is

\[ \begin{array}{1 1}(1)45^{\circ}&(2)30^{\circ}\\(3)60^{\circ}&(4)90^{\circ}\end{array}\]

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A)
The equation of the given parabola is $y^2=16 x$
$y^2=4(4)x=>a=4$
The equation of any tangent to the parabola $y^2=16x$ is
$y= mx +\large\frac{4}{m}$
This passes through the point $(-4,4)$
$4= -4m + \large\frac{4}{m}$
$1=-m +\large\frac{1}{m}$
$m=-m^2+1$
$m^2+m-1=0$
Let $m_1,m_2$ be the slopes of the tangents
Then product of the slopes $m_1.m_2 =\large\frac{-1}{1}$$=-1$
$90^{\circ}$ is the correct answer.
Hence 4 is the correct answer.
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