List of top Mathematics Questions on Tangents and Normals asked in MET

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

The equation of the tangent to the curve $\left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2$ at $(a, b)$ is

The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal on the $x$-axis passing through $(2,1)$, is