Find the equation of the tangent to the curve $y=\sqrt{3x-2}$ which is parallel to the line $4x-2y+5=0$.

The angle of intersection of the curves $r = \sin \theta + \cos \theta$ and $r = 2 \sin \theta$ is equal to:

Find the point on the curve $y=x^{3}-11x+5$ at which the tangent is $y=x-11$.

If the point $P(x_1, y_1)$ lying on the curve $y = x^2 - x + 1$ is the closest point to the line $y = x - 3$, then the perpendicular distance from $P$ to the line $3x + 4y - 2 = 0$ is

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

Tangents are drawn to the curve $y = \sin x$ from the origin. The locus of the points of contact is