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  • The shortest distance between the line and the curve is :

The shortest distance between the line x - y = 1 and the curve x^2 = 2y is :
Option: 1 \frac{1}{2}
Option: 2 \frac{1}{2\sqrt{2}}
Option: 3 \frac{1}{\sqrt{2}}
Option: 4 0

Answers (1)

best_answer

The shortest distance between curves is always along common normal.

the slope of the line

\frac{dy}{dx}=1=\text{slope of the line}

P is any point on the parabola, and also tangent pass through point P

slope of the tangent to the parabola 

\\2x=2\frac{dy}{dx}\\\frac{dy}{dx}=x=1\\\Rightarrow y=\frac{1}{2}

\text{Point P}=\left ( 1,\frac{1}{2} \right )

\therefore \text { Shortest distance }=\left|\frac{1-\frac{1}{2}-1}{\sqrt{1^{2}+1^{2}}}\right|=\frac{1}{2 \sqrt{2}}

 

Posted by

himanshu.meshram

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