Tangents and it...

If the tangent at each point of the curve $$\displaystyle y=\frac { 2 }{ 3 } { x }^{ 3 }-2a{ x }^{ 2 }+2x+5$$ makes an acute angle with the positive direction of x-axis, then 

If a variable tangent to the curve $$\displaystyle x^2y = c^3$$ makes intercepts a, b on x and y axis respectively, then the value of $$\displaystyle a^2b$$ is

If $$y = 4x - 5$$ is a tangent to the curve $$\displaystyle y^2 = px^3 + q$$ at $$(2, 3)$$, then

The slope of the tangent to the curve $$y=x^{2}-x$$ at the point where the line $$y=2$$ cuts the curve in the first quadrant is

If the tangent to the curve $$xy + ax + by = 0$$ at (1, 1) makes an angle $$\displaystyle \tan ^{-1}(2)$$ with x-axis, then $$\displaystyle a + 2b$$ is equal to

If at each point of the curve $$y=x^{3}-ax^{2}+x+1$$ the tangent is inclined at an acute angle with the positive direction of the x-axis then

The slope of the tangent to the curve $$y=\sqrt{4-x^{2}}$$ at the point where the ordinate and the abscissa are equal, is

If the tangent to the curve $${ 2y }^{ 3 }={ ax }^{ 2 }+{ x }^{ 3 }$$ at the point $$(a,a)$$ cuts off intercepts $$\alpha $$ and $$\beta $$ on the coordinate axes such that $${ \alpha  }^{ 2 }+{ \beta  }^{ 2 }=61,$$ then $$a=$$

If $$m$$ be the slope of a tangent to the curve $${ e }^{ 2y }=1+4{ x }^{ 2 }$$, then 

If $$m$$ be the slope of tangent to the curve $$e^{y}=1+x^{2}$$ then