Tangents and it...

The equation of tangent to the curve $$\sqrt {x}+ \sqrt {y}= \sqrt {a}$$ at the point $$\left( { x }_{ 1 },{ y }_{ 1 } \right) $$ is-

The equation normal to the curve $$x^{2/3}+y^{2/3}=a^{2/3}$$ at the point $$(a, 0)$$ is-

The normal to the curve $$y(x - 2)(x - 3) = x + 6$$ at the point where the curve intersects the y-axis passes through point 

The equation of the tangent to the curve $$y = 2\sin x + \sin 2x$$ at $$x = \dfrac{\pi}{3}$$ on it is

Equation of normal drawn to the graph of the function defined as $$f(x)=\cfrac{\sin{x}^{2}}{x},x\ne 0$$ and $$f(0)=0$$ at the origin is

The equation of tangent to the curve $$y=\dfrac{x+9}{x+5}$$ so that is passes through the origin is

The curve y$$=ax^3+bx^2+cx+5$$ touches the x-axis at $$P(-2, 0)$$ then $$C=?$$

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

If the curves $$\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{4}=1$$ and $$y^{2}=16x$$ intersect at right angles then value of $$a^{2}$$ is

Slope of the line $$ \sqrt { { x }^{ 2 }+{ 4y }^{ 2 }-4xy+4 } +x-2y=1$$ equals to