Tangents and it...

At what point of the curve $$\displaystyle y=2x^{2}-x+1$$ tangent is parallel to $$y = 3x + 4$$

The slope of the normal to the curve $$\displaystyle x=a\left ( \theta -\sin \theta  \right ),\: \: y=a\left ( 1-\cos \theta  \right )$$ at point $$\displaystyle \theta =\dfrac{\pi }2$$ is

A tangent to the hyperbola $$\displaystyle y=\frac { x+9 }{ x+5 } $$ passing though the origin is

The normal to the curve $$\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}$$ is perpendicular to $$x$$ axis at the point

If equation of normal at a point $$\displaystyle \left ( m^{2},-m^{3} \right )$$ on the curve $$\displaystyle x^{3}-y^{2}=0\: \: is\: \: y=3mx-4m^{3}$$ then $$\displaystyle m^{2}$$ equals

The slope of the tangents to the curve $$y = (x + 1) (x - 3)$$ at the points where it crosses x - axis are

The slope of normal to the curve $$\displaystyle y^{2}=4ax$$ at a point $$\displaystyle \left ( at^{2},2at \right )$$ is

The slope of the tangent to the curve $$xy + ax - by = 0$$ at the point $$(1, 1)$$ is $$2$$ then values of $$a$$ and $$b$$ are respectively -

The coordinates of the points on the curve $$\displaystyle x=a\left ( \theta +\sin \theta  \right ),y=a\left ( 1-\cos \theta  \right )$$ where tangent is inclined an angle $$\displaystyle \dfrac{\pi }4$$ to the $$x-$$axis are -

If the curve $$y^2=ax^3-6x^2+b$$ passes through $$(0,\,1)$$ and has its tangent parallel to y-axis at $$x=2$$, then