Tangents and it...

The slope of the tangent to the curve $$y= \sqrt {4-x^2}$$ at the point where the ordinate and the abscissa are equal is

The curve given by $$x+y=e^{xy}$$ has a tangent parallel to the y-axis at the point

If the parabola $$y = ax^2 - 6x + b$$ passes through $$(0, 2)$$ and has its tangent at $$x = \dfrac{3}{2}$$ parallel to the $$x-$$axis then

The normal to the curve $$2x^2 +y^2=12$$  at the point $$(2,2)$$ cuts the curve again at

At what points of curve $$y= \displaystyle \frac {2}{3} x^3 + \displaystyle \frac{1}{2} x^2 $$, the tangent makes equal angle with the axis

If $$x+ 4y=14$$ is a normal to the curve $$y^2=\alpha x ^3-\beta $$ at $$(2,3)$$, then the value of $$\alpha+\beta$$ is

If a variable tangent to the curve $$x^2y=c^3$$ makes intercepts $$a , b$$ on $$X$$-axes and $$Y$$- axes, respectively, then the value of $$a^2b$$ is

The equation of the tangent to the curve $$y=be^{-x/a}$$ at the point where it crosses the $$y$$-axis is

The point(s) at each of which the tangents to the curve $$\displaystyle y = x^3 - 3x^2 - 7x + 6$$ cut off on the positive semi axis $$OX$$ a line segment half that on the negative semi axis $$OY$$, then the co-ordinates of the point(s) is/are give by:

A line L is perpendicular to the curve $$\displaystyle  y = \dfrac {x^2}{4} - 2$$ at its point P and passes through (10, -1). The coordinates of the point P are