Application of ...

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 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

If $$g\left( x \right) =2f\left( 2{ x }^{ 3 }-3{ x }^{ 2 } \right) +f\left( 6{ x }^{ 2 }-4{ x }^{ 3 }-3 \right)$$ $$\forall \ x\ \in \ R$$ and $$f^{''}\left( x \right) > 0$$, $$\forall \ x \in \ R$$, then $$g\left ( x \right)$$ is increasing in the interval

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

The slope of the tangent to the curve $$y=\int _{ 0 }^{ x }{ \frac { dt }{ 1+{ t }^{ 3 } }  } $$ at the point where $$x=1$$ 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 area of the triangle formed by the positive x-axis, the tangent and normal to the curve $${ x }^{ 2 }+{ y }^{ 2 }=16{ a }^{ 2 }$$ at the point $$\left( 2\sqrt { 2 } a,2\sqrt { 2 } a \right) $$ is

A tangent PT is drawn to the circle $$x^2+y^2=4$$ at the point $$P(\sqrt{3}, 1)$$. A straight line L, perpendicular to PT is a tangent to the circle $$(x-3)^2+y^2=1$$. $$(1)$$ A possible equation of L is?