Find the equation of tangent to the circle x² +y² + 2x - 3y - 8 = 0 at (2, 3).

Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

If the line y = 3x + 1, touches the parabola y² = 4ax, find the length of the latus rectum?

For the ellipse x² + 3y² = a², find the length of major and minor axis.

Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.