The symmetry in the curve $x^3 + y^3 = 3axy$ is along:

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed $1$,then the range of '$a$' is

If curves $y = ax^2 + bx + c$ and $y = px^2 + qx + r$ do not intersect each other and $a, b, c, p, q, r \in \{1, 2, 3, 4, \dots, 10\}$,then the maximum value of $(aq - bp)^2 + (c - r)^2$ is-

For the curve $x^{2}+4xy+8y^{2}=64$, the tangents are parallel to the $x$-axis only at the points

If the chord through $(1, -2)$ cuts the curve $3x^2 - y^2 - 2x + 4y = 0$ at $P$ and $Q$,then the angle subtended by $PQ$ at the origin is (in $^{\circ}$)

If the point $(2, -3)$ lies on the curve $kx^2 - 3y^2 + 2x + y - 2 = 0$,then $k$ is equal to: