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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 tangent to the ellipse at that point then the point where the particle crosses the Y-axis is

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$(0, \frac{- 25}{3})$

$(0, \frac{7}{3})$

$(0, \frac{25}{3})$

$(0, 9)$

answer is B.

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Detailed Solution

$\frac{x^{2}}{100} + \frac{y^{2}}{25} = 1$

Equation of tangent at (-8,3) is

$\frac{{xx}_{1}}{100} + \frac{{yy}_{1}}{25} = 1$

$\frac{- 8 x}{100} + \frac{3 y}{25} = 1$

$2 x - 3 y = - 25$

x=0 on y-axis

$y = \frac{25}{3}$

$(0, \frac{25}{3})$

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