Tangents and it...

The equation of normal of $$x^2+y^2-2x+4y-5=0$$ at $$(2,\,1)$$ is

The equation of tangent to the curve $$y=3{ x }^{ 2 }-x+1$$ at the point $$(1,3)$$ is

The equation of tangent to the curve $$y = x^{2} + 4x + 1$$ at $$(-1, -2)$$ is 

The slope of the normal to the curve $$y = 3x^2$$ at the point whose $$x$$-coordinate $$2$$ is

The slope of the tangent to the curve $$y=3{ x }^{ 2 }+3\sin { x } $$ at $$x=0$$ is

The equation of the normal to the curve $$\theta =\dfrac { 1 }{ t } $$ at the point $$\left( -3,-\dfrac { 1 }{ 3 }  \right) $$ is:

The tangent to the curve $$y=x^3+1$$ at (1, 2) makes an agnle $$\theta$$ with y axis, then the value of tan $$\theta$$ is.

What is the slope of the tangent to the curve $$ x = t^2 + 3t - 8, y = 2t^2 - 2t - 5$$ at t = 2 ?

If the tangent to the function $$y = f(x)$$ at $$(3, 4)$$ makes an angle of $$\dfrac {3\pi}{4}$$ with the positive direction of x-axis in anticlockwise direction then $$f'(3)$$ is

The equation of tangent to the curve $$y = 3x^{2} - x + 1$$ at $$P(1, 3)$$ is ____