Tangents and it...

If the tangent to the curve $$\sqrt{x}+\sqrt{y}=\sqrt{a}$$ at any points on it cuts the axes $$OX$$ and $$OY$$ at $$P$$ and $$Q$$ respectively then $$OP+OQ$$ is

The curve $$\displaystyle \frac{x^{n}}{a^{n}}+\frac{y^{n}}{b^{n}}=2$$ touches the line $$\displaystyle \frac{x}{a}+\frac{y}{b}=2$$ at the point

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

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

The area bounded by the axes of reference and the normal to $$y=\log_{e}x$$ at the point $$(1, 0)$$ is

If the line joining the points $$(0, 3)$$ and $$(5, -2)$$ is the tangent to the curve $$\displaystyle y=\frac{c}{x+1}$$ then the value of $$c$$ is

The sum of the intercepts made on the axes of coordinates by any tangent to the curve $$\sqrt{x}+\sqrt{y}=2$$ is equal to

The triangle formed by the tangent to the curve $$\displaystyle f(x)=x^{2}+bx-b$$ at the point $$(1, 1)$$ and the coordinates axes, lies in the first quadrant. If its area is $$2$$ then the value of b is

Angle between the tangents to the curve $$y= x^{2}-5x+6$$ at the points $$(2,0)$$ and $$\left ( 3,0 \right )$$ is

The number of tangents to the curve $$\displaystyle y= e^{\left | x \right |}$$ at the point $$(0,1)$$ is