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  • Find the angle subtended at the origin by the chord <img alt="\mathrm{4 p x-\sqrt{2} p y=4 \sqrt{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B4%20p%20x-%5Csqrt%7B2%7D%

Find the angle subtended at the origin by the chord \mathrm{4 p x-\sqrt{2} p y=4 \sqrt{2}} b of the curve \mathrm{p x^2-4 b y=0}.

Option: 1

\frac{\pi}{3}


Option: 2

\frac{\pi}{4}


Option: 3

\frac{\pi}{2}


Option: 4

\frac{5\pi}{12}


Answers (1)

best_answer

Curve : \mathrm{p x^2-4 b y=0}

Homogenizing the equation of the curve with given chord \mathrm{\frac{p}{\sqrt{2} b} x-\frac{p}{4 b} y=1}

\mathrm{p x^2-4 b y\left(\frac{p}{\sqrt{2 b}} x-\frac{p}{4 b} y\right)=0}

\mathrm{\Rightarrow p x^2-2 \sqrt{2} p x y+p y^2=0} 

which is a pair of straight lines passing through O(0, 0) 

Angle \mathrm{\theta=\tan ^{-1}\left(\frac{2 \sqrt{2 p^2-p^2}}{p+p}\right)=\frac{\pi}{4}}

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vinayak

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