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TS EAMCET · Maths · Ellipse

A particle is travelling in clockwise direction on the ellipse \(\frac{x^2}{100}+\frac{y^2}{25}=1\). If the particle leaves the ellipse at the point \((-8,3)\) on it and travels along the tangents to the ellipse at that point then the point where the particle crosses the \(\mathrm{Y}\)-axis is

  1. A \(\left(0, \frac{7}{3}\right)\)
  2. B \(\left(0, \frac{25}{3}\right)\)
  3. C \((0,9)\)
  4. D \(\left(0, \frac{-25}{3}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left(0, \frac{25}{3}\right)\)

Step-by-step Solution

Detailed explanation

\(\frac{x^2}{100}+\frac{y^2}{25}=1\) Equation of tangent at \((-8,3)\) \(\begin{aligned} & \frac{-8 x}{100}+\frac{3 y}{25}=1 \Rightarrow-8 x+12 y=100 \\ \Rightarrow \quad & 2 x-3 y+25=0 \end{aligned}\) For point at \(y\) axis, \(x=0\)…