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  • Tangent and narmal are drawn at on the parabola <img alt="\mathrm{y^2=16 x}" src=

Tangent and narmal are drawn at \mathrm{P(16,16)} on the parabola \mathrm{y^2=16 x}, which intersect the axis of the purabola at \mathrm{A\: and \: B}, respectively. If  \mathrm{C} is the centre of the circle through the points \mathrm{P,} \mathrm{A\: and \: B} and \mathrm{\angle C P B=\theta}, then a value of  \mathrm{\tan \theta} is

Option: 1

2


Option: 2

0


Option: 3

1


Option: 4

4


Answers (1)

best_answer

The equation of tangent at \mathrm{P(16,16)\: is \: x-2 y+16=0}

The equation of normal at \mathrm{P(16,16)\: is \: 2 x+y-48=0}

The slope of \mathrm{P C: m_1=\frac{16}{12}=\frac{4}{3}}

The slope of \mathrm{P B: m_2=\frac{-16}{8}=-2}

\mathrm{ \tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right|=\left|\frac{\frac{4}{3}+2}{1-\frac{4}{3}(2)}\right|=\left|\frac{\frac{10}{3}}{-\frac{5}{3}}\right|=2 }


 

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