Tangents and it...

If the slope of one of the lines represented $${a^3}{x^2} + 2hxy + {b^3}{y^2} = 0$$ be the square of the other, then $$ab(a+b)$$ is equal to:

Slope of tangent to the circle $$( x - r ) ^ { 2 } + y ^ { 2 } = r ^ { 2 }$$ at the point $$( x , y )$$ lying on the circle is

The slope of the straight line which is both tangent and normal to the curve $$4x^3=27y^2$$ is 

The angle between the curves $$y = \sin x$$ and $$y = \cos x$$ is 

The tangent at any point of the curve $$x={ at }^{ 3 },y={ at }^{ 4 }$$ divides the abscissa of the point of contact in the ratio

The tangent to the curve $$y=e^{2x}$$ at the point $$(0, 1)$$ meets x-axis at?

The tangent to the curve, $$y = xe^{x^2}$$ passing through the point $$(1, e)$$ also passes through the point:

Three normals are drawn from the point $$\left(c,0\right)$$ to the curve $${y}^{2}=x.$$If two of the normals are perpendicular to each other,then $$c=$$

If the line $$x+y=0$$ touches the curve $$2y^2=\alpha x^2+\beta $$ at $$(1,-1),$$ then $$(\alpha ,\beta )=$$

Equation of the tangent at (1, -1) to the curve
$${ x }^{ 3 }-x{ y }^{ 2 }-4{ x }^{ 2 }-xy+5x+3y+1=0$$ is