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Prove that the curves x=y^2 and …

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Prove that the curves x=y^2 and xy=k cut at right angles if 8k^2 =1

Posted by Yash Kalra 5 years, 8 months ago

CBSE > Class 12 > Mathematics

3 answers

Jqiqiq 71U1Uq 5 years, 8 months ago

✨❤️❤️✨❤️❤️✨ ❤️❤️❤️❤️❤️❤️❤️ ❤️❤️❤️❤️❤️❤️❤️ ✨❤️❤️❤️❤️❤️✨ ✨✨❤️❤️❤️✨✨ ✨✨✨❤️✨✨✨

Ritochit Bose 5 years, 8 months ago

x=y^2 ----(eq1) xy=k ----(eq2) Now, from eq1 —> dy/dx = 1/2y from eq2 —> dy/dx = -y/x We know, condition for cutting at right angles — m1 x m2 = -1 => 1/2y x (-y/x) = -1 => 2x=1 => x= 1/2 Putting x=1/2 in eq1 we get, y=√x =1/√2 Now, putting x=1/2 and y=1/√2 in eq2 we get, 1/2 x 1/√2 = k => 2√2k=1 squaring both sides— 8k^2=1. Hence proved. Hope this helps you!

Rajat Barwar 5 years, 8 months ago

Find dy/dx from both equation and make their product equal to -1. Hope it may help you...

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