Slope of normal drawn to the ellipse at a point P is 34 and eccentricity of the ellipse is 13 If this normal makes an acute angle β with its focal chord through P then the absolute value of 5sinβ is________

sin⁡α=PMPNsin⁡β=PSPNsin⁡βsin⁡α=PSPN=13sin⁡β=13sin⁡α,=13,35=15

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Slope of normal drawn to the ellipse at a point $P$ is $\frac{3}{4}$ and eccentricity of the ellipse is $\frac{1}{3}$ If this normal makes an acute angle $β$ with its focal chord through $P$ then the absolute value of $5 \sin β$ is________

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Detailed Solution

$\begin{array}{l} \sin α = \frac{P M}{P N} \\ \sin β = \frac{P S}{P N} \\ \frac{\sin β}{\sin α} = \frac{P S}{P N} = \frac{1}{3} \\ \sin β = \frac{1}{3} \sin α, = \frac{1}{3}, \frac{3}{5} = \frac{1}{5} \end{array}$

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