Tangents and it...

A normal to parabola, whose inclination is $$30^o$$, cuts it again at an angle of.

If the slope of the tangent to the curve $$y=a{ x }^{ 3 }+bx+4$$ at $$(2,14) = 21$$, then the values of $$a$$ and $$b$$ are respectively

The angle between the curves $$x^{2} + y^{2} = 25$$ and $$x^{2} + y^{2} - 2x + 3y - 43 = 0$$ at $$(-3, 4)$$ is

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

The equation of the tangent to the curve $$y=\sqrt { 9-2{ x }^{ 2 } } $$ as the point where the ordinate and the abscissa are equal , is 

The equation of the curve satisfying the differential equation $$y_{2}(x^{2} + 1) = 2xy_{1}$$ passing through the point $$(0, 1)$$ and having slope of tangent at $$x = 0$$ as $$3$$ is

The slope of the tangent at each point of the curve is equal to the sum of the coordinate of the point. Then, the curve that passes through the origin is

The equation of tangent to the curve $${ \left( \cfrac { x }{ a }  \right)  }^{ n }+{ \left( \cfrac { y }{ b }  \right)  }^{ n }=2\quad $$ at the point $$(a,b)$$ is

The slope of the tangent at the point $$(h, h)$$ of the circle $$x^{2} + y^{2} = a^{2}$$ is :

The angle at which the curve $$y={ x }^{ 2 }$$ and the curve $$x=\cfrac { 5 }{ 3 } \cos { t } ,y=\cfrac { 5 }{ 4 } \sin { t } $$ intersect is