Tangents and it...

Normal to the curve $$\displaystyle x^{2}=4y$$ which passes through the point $$(1,2)$$

Find the equation of a line passing through $$(-2,3)$$ and parallel to tangent at origin for the circle $$\displaystyle x^{2}+y^{2}+x-y=0$$

Find the equations of tangents to parabola $$\displaystyle y^{2}= 4ax$$ which are drawn from the point (2a,3a).

The normal drawn at the point $$\displaystyle P\left ( at_{1}^{2},2at_{1} \right )$$ on the parabola meets the curve again at$$\displaystyle Q\left ( at_{2}^{2},2at_{2} \right ).$$ then $$\displaystyle t_{2} =?$$

The slope of the tangent to the curve $$\displaystyle y=-x^{3}+3x^{2}+9x-27$$ is maximum when x equals.

Find the tangents and normal to the curve $$y(x-2)(x-3)-x+7=0,$$ at point (7,0) are 

Find the distance between the point $$(1,1)$$ and the tangent to the curve $$\displaystyle y=e^{2x}+x^{2}$$ drawn from the point where the curve cuts $$y$$-axis

The curve $$\displaystyle y-e^{xy}+x=0$$ has a vertical tangent at

Find the equation of the tangent to the curve $$\displaystyle y=x^{2}+1$$ at the point $$(1,2).$$

The point on the curve $$\displaystyle y=x^{2}-3x+2$$ at which the tangent is perpendicular to the line $$y = x$$ is -