Find the length of the tangent from (2, -3) to the circle x² + y² - 8x - 9y + 12 = 0.

If a parabolic reflector is 24 cm in diameter and 6 cm deep, find its locus.

Find the locus of a point which divides so that the sum of its distances from (-4, 0) and (4, 0) is 10 units.

Find the eccentricity of the ellipse with foci on x-axis if its latus rectum be equal to one half of its major axis.

Find the equation of the hyperbola whose vertices are (0, ±7) and e = \(\frac { 4 }{ 3 } \)