Tangents and it...

The curve $$y = ax^3 + bx^2 + cx + 8$$ touches $$x-$$ axis at $$P(-2, 0)$$ and cuts $$y-$$ axis at a point $$Q$$ where its gradient is $$3$$. The values of $$a, b, c$$ are respectively ?

The equation of the normal to the curve $$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$$ at the point $$(x_1, y_1)$$ on it is?

The curve satisfying D.E $$y dx - (x+3{y}^{2})dy=0$$ and passing through the point $$(1,1)$$ also passes through the point:

Area of the triangle formed by the tangent, normal to the curve $$x^{2}/a^{2}+y^{2}/b^{2}=1$$ at the point $$(a/\sqrt{2} , b/\sqrt{2})$$ and the $$x-$$axis is

The numbers of tangent to the curve $$y - 2 = {x^5}$$  which are drawn
from point $$\left( {2,2} \right)$$ is/are 

Equation of a normal to the curve $$y=x\log{x}$$, parallel to $$2x-2y+3=0$$ is

If the normal to the curve $$y=f\left( x \right)$$ at $${(3,4)}$$ makes angle $$\dfrac {3\pi}{4}$$ with $$\bar {OX}$$ then $$f^{ 1 }\left( 3 \right)=$$

Equation of a tangent to the curve $$y=\cos(x+y),\ 0\le x\le 2\pi$$ that is parallel to the line $$x+2y=0$$ is

The equation of normal to the curve $$x^{3}+y^{3}=8xy$$ at points where it is meet by the curve $$y^{2}=4x$$,other then origin is

Tangents are drawn from a point on the circle $$x^2+y^2=25$$ to the ellipse $$9x^2+16y^2-144=0$$ then the angle between the tangents is