The semi-major axis is 4 and the semi-minor axis is 3 after rewriting the equation in standard form.

The distance between the foci of the hyperbola is 2c, where c = √(a^2 + b^2) = √(25 + 16) = √41, so the distance is 2√41.

The equation of a parabola with directrix y = -p is y^2 = -4px.

The eccentricity of a parabola is always equal to 1.

In the equation y^2 = 4px, p = 3, hence the value of 'p' is 3.

The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is y^2/a^2 + x^2/b^2 = 1.

The directrix of the parabola y^2 = 8x is given by x = -2.

For the ellipse x^2/16 + y^2/9 = 1, the foci are located at (±4, 0) where c = √(16 - 9) = 4.

The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at (±3, 0).

The distance between the foci is 6, calculated using the formula 2c where c = √(a^2 - b^2).

The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.

The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).

The equation of a circle with center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

The directrix of the parabola x^2 = 8y is y = -2.

The equation of the ellipse is x^2/25 + y^2/9 = 1.

The length of the latus rectum of the ellipse is given by 2a^2/b.

The length of the latus rectum of the parabola y^2 = 4ax is 4a.

The length of the latus rectum of the parabola y^2 = 8x is 4.

The standard form of a parabola that opens upwards is given by x^2 = 4ay.

The equation of a hyperbola with transverse axis along the x-axis is x^2/a^2 - y^2/b^2 = 1.

The equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a) is y^2/a^2 + x^2/b^2 = 1.

The equation x^2/a^2 - y^2/b^2 = 1 represents a hyperbola with transverse axis along the x-axis.