Application of ...

If the curves $${y}^{2}=6x,9{x}^{2}+b{y}^{2}=16$$ intersect each other at right angles, then the values of $$b$$ is

The equation of normal to the curve $$y=\left| { x }^{ 2 }-\left| x \right|  \right| $$ at $$x=-2$$ is

If the tangent to the curve $$y=x\log { x } $$ at $$\left( c,f\left( x \right)  \right) $$ is parallel to the line-segment joining $$A\left(1,0\right)$$ and $$B\left(e,e\right)$$, then c=...... .

The intercept on x-axis made by tangent to the curve, $$\displaystyle y=\int _{ 0 }^{ x }{ \left| t \right|  } dt,x\in R$$, which are parallel to the line $$y=2x$$, are equal to

The slope of the tangent to the curve $$y=sinx$$ where it crosses the $$x-axis$$ is 

The Point (s) on the cure $${ y }^{ 3 }+{ 3x }^{ 2 }=12y$$ where the tangent is vertical (parallel to y-axis), is/are.

The angle made by the tangent line at (1, 3) on the curve $$y=4x-{ x }^{ 2 }$$ with $$\overset { - }{ OX } $$ is 

equation of tangent at $$(0,0)$$ for the equation $$y^2=16x$$

The area of triangle formed by tangent and normal at point $$(\sqrt{3}, 1)$$ of the curve $$x^2+y^2=4$$ and x-axis is?

The function $$f(x)=x^3-6x^2+9x+3$$ is decreasing for