Subjective Type

Find the shortest distance of the point (0,c) from the parabola $$y = x^{2}$$, where $$0\leq c \leq 5$$.

Solution

SIMILAR QUESTIONS

Application of Derivatives

The shortest distance between the line $$y-x =1$$ and the curve $$\mathrm{x}=\mathrm{y}^{2}$$ is

Application of Derivatives

The shortest distance between line $$y-x =1$$ and curve $$\mathrm{x}=\mathrm{y}^{2}$$ is

Application of Derivatives

The point $$(0, 5)$$ is closer to the curve $$\displaystyle { x }^{ 2 }=2y$$ at:

Application of Derivatives

The shortest distance between the parabolas $${ y }^{ 2 }=4x$$ and $${ y }^{ 2 }=2x-6$$ is

Application of Derivatives

The coordinates of the point on the parabola $$\displaystyle y^{2}=8x,$$ which is at minimum distance from the circle $$\displaystyle x^{2}+\left ( y+6 \right )^{2}=1$$ are

Application of Derivatives

On the parabola $$y={ x }^{ 2 },$$ the point at a least distance from the straight line $$y=2x-4$$ is

Application of Derivatives

Minimum distance between the curves $$y^2=4x\;\&\;x^2+y^2-12x+31=0$$ is

Application of Derivatives

The number of point in the rectangle $$\{(x,y);$$ $$−12\le x \le12$$ and $$−3\le y\le3\}$$ which lie on the curve $$y=x+\sin x$$ and at which in the tangent to the curve is parallel to the $$x-axis$$ is

Application of Derivatives

If d is the minimum distance between the curves $$f(x)=e^{x}$$ and $$g(x) = log_{e}x,$$ then the value of $$d^{6}$$ is

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