Application of ...

$$P(2, 2)$$ and $$Q\left ( \displaystyle \frac{1}{2}, -1 \right )$$ are two points on the parabola $$y^{2}=2x$$. The coordinates of the point $$R$$ on the parabola, where tangent to the curve is parallel to the chord $$PQ$$ is

The number of tangents to the curve $$y^{2}-2x^{3}-4y+8=0$$ that pass through $$(1, 0)$$ 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

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

If error in  measuring the edge of a cube is $$k$$% then the percentage error in estimating its volume is

The point on the curve $$\sqrt{x}+\sqrt{y}=2a^{2}$$, where the tangent is equally inclined to the axes, is

The angle between two tangents to the ellipse $$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{9}=1$$ at the points where the line $$y=1$$ cuts the curve 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

The curve $$y+e^{xy}+x= 0$$ has a tangent parellel to y-axis at a point