Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Tangent and normal are drawn at $P(16,16)$ on the parabola $y^2=16 x$ which intersect the axis of the parabola at A and B, respectively. If C is the center of the circle through the points P, A and B and ∠ = CPB θ, then a value of tanθ is
Option: 1
$\begin{aligned} & \frac{1}{2} \\ \end{aligned}$

Option: 2
$-\frac{10}{9} \\$

Option: 3
$3 \\$

Option: 4
$\frac{4}{3}$

Answers (1)

best_answer

Equation of tangent and normal to the curve $y^2=16 x \text { at } P(16,16) \text { is } x-2 y+16=0$ and $2 x+y-48=0 .$

$A=(-16,0) ; B=(24,0)$

$\because$ C is the center of circle passing through PAB i.e. $c(4,0)$

Slope of $\begin{aligned} & P C=\frac{16-0}{16-4}=\frac{4}{3}=m_1 \\ \end{aligned}$

Slope of $P B=\frac{16-0}{16-24}=\frac{16}{8}=-2=m_2$

$\begin{aligned} & \tan \theta=\frac{m_1-m_2}{1+m_1 m_2} \\ & \Rightarrow \tan \theta=\frac{\frac{4}{3}+2}{1-\frac{4}{3}(2)} \\ & \Rightarrow \tan \theta=-\frac{10}{9} \end{aligned}$

Posted by

Pankaj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Latest Question