The line $y = mx + 1$ is a tangent to the parabola $y^2 = 4x$. Find the value of $m$.

The equation of a parabola which passes through the intersection points of the straight line $x + y = 0$ and the circle $x^2 + y^2 + 4y = 0$ is:

If the coordinates of the ends of a focal chord of the parabola $x^2=4ay$ are $(x_1, y_1)$ and $(x_2, y_2)$,then

Two parabolas $x = cy^2 + ay + b$ and $x = cy - y^2$ touch each other at the point $(0, 1)$. Then the value of $2a + b - c$ is:

Find the parameter $t$ for the point $(4, -6)$ on the parabola $y^2 = 9x$.

The axis of the parabola $x^{2}+2 x y+y^{2}-5 x+5 y-5=0$ is