EllipseHardBloom L3
Question
Consider the particle travelling clockwise on the elliptical path $\frac{x^{2}}{100} + \frac{y^{2}}{25} = 1$. The particle leaves the orbit at the point $( - 8,3)$ and travels in a straight line tangent to the ellipse. At what point will the particle cross the $y$-axis ?
Options
A.$\left( 0,\frac{25}{3} \right)$
B.$\left( 0, - \frac{25}{3} \right)$
C.$(0,9)$
D.$\left( 0,\frac{7}{3} \right)$
Solution
Sol.(a) Equation of tangent at $( - 8,3)$ is
$$\frac{x( - 8)}{100} + \frac{y(3)}{25} = 1$$
$$\text{~}\text{Put}\text{~}\ x = 0$$
$\Rightarrow \ $ Y = 25/3
$\Rightarrow$ Q = (0, 25/3)
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