Find the center of the conic $14x^2 - 4xy + 11y^2 - 44x - 58y + 71 = 0$.

The equation $\frac{x^2}{1 - r} - \frac{y^2}{1 + r} = 1$ for $r > 1$ represents:

Find the centre of the conic section represented by the equation $14x^2 - 4xy + 11y^2 - 44x - 58y + 71 = 0$.

Which of the following equations does not represent a hyperbola?

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-

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 $^{\circ}$)