Find the length of tangent of parabola $y^{2} = 4 x$ at $(1, 1)$ .

2 \sqrt{2}

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2 \sqrt{5}

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2 \sqrt{6}

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2 \sqrt{9}

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Solution

The correct option is A $2 \sqrt{2}$
Length of tangent to parabola is $| y \sqrt{1 + {(\frac{d x}{d y})}^{2}} |$
The equation of parabola is $y^{2} = 4 x$
Differentiate w.r.t $y$ , we get $\frac{d x}{d y} = \frac{y}{2}$
The point at which we have to find length of tangent is $(1, 2)$
The length of tangent is $| y \sqrt{1 + \frac{y^{2}}{4}} | = 2 \sqrt{1 + 1} = 2 \sqrt{2}$
Therefore, the correct option is $A$

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Find the length of tangent of parabola y2=4x at (1,1).

The correct option is A 2√2Length of tangent to parabola is |y√1+(dxdy)2|The equation of parabola is y2=4xDifferentiate w.r.t y, we get dxdy=y2The point at which we have to find length of tangent is (1,2)The length of tangent is |y√1+y24|=2√1+1=2√2Therefore, the correct option is A

Find the length of tangent of parabola $y^{2} = 4 x$ at $(1, 1)$ .