JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Tangent and normal are drawn at \(P(16, 16)\) on the parabola \({y^2} = 16x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points \(P, A\) and \(B\) and \(\angle CPB = \theta \) , then a value of \(\tan \theta \;\)is :
- A \(2\)
- B \(3\)
- C \(\frac{4}{3}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Slope of \(PC\left( {{m_1}} \right) = \frac{4}{3}\) Slope of \(PB\left( {{m_2}} \right) = - 2\) Hence, \(\tan \theta = \left| {\frac{{{m_1} - {m_2}}}{{1 + {m_1}.{m_2}}}} \right| = \left| {\frac{{\frac{4}{3} + 2}}{{1 - \frac{4}{3}.2}}} \right|\) \(\tan \theta = 2\)
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