The equation of the tangent to the curve $y=5x^2-3x+7$ at the point $(-1, 4)$ is:

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

The angle of intersection of curves $y = x^2$ and $6y = 7 - x^3$ at the point $(1, 1)$ is:

If the relation between the subnormal $SN$ and the subtangent $ST$ at any point $S$ on the curve $by^2 = (x + a)^3$ is $p(SN) = q(ST)^2$,then what is the value of $p/q$?

The length of the subtangent to the curve $\sqrt{x} + \sqrt{y} = 3$ at the point $(4, 1)$ is

The abscissa of the point on the curve $\sqrt{xy} = a + x$ where the tangent cuts off equal intercepts from the coordinate axes is $(a > 0)$.