- ) L Q22) A rod AB of length 15 cm...
Question

# - ) L Q22) A rod AB of length 15 cm rests in between two coordinate axis in such a way that the end point A lies on x-axis and end point B lies on y-axis. A point P is taken on the rod in such a way that AP = 6cm. If the locus of P is an ellipse, then its eccentricity(e) is: 1) VS 2) 47 4) JE 3)

JEE/Engineering Exams
Maths
Solution
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Giren ( A B=15 mathrm{cm} ) ( A P=6 mathrm{cm} ) ( angle P A R=theta ) in ( triangle B P Q ) ( cos theta=frac{x}{9} ) ( ln Delta P A R ) ( sin theta=frac{y}{6} ) ecentricity ( =frac{c}{9} quad sin ^{2} theta+cos ^{2} theta=1 ) ( c^{2}=a^{2}-b^{2} quad frac{y^{2}}{36}+frac{x^{2}}{81}=1 ) ( c^{2}=2 pi cos 45 ) y eghation of ellipy ( e=q ) ( therefore ) locus of ( P ) is ( c=3 sqrt{5} ) ( e=frac{c}{a}=frac{beta sqrt{5}}{93}=frac{sqrt{5}}{3} )