Conic Sections

What is the standard equation of a circle with center at the origin and radius r?

Which conic section is represented by the equation x² - y² = 1?

The eccentricity of a parabola is always:

If the equation of an ellipse is \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \), what is its eccentricity?

The directrix of the parabola \( y^2 = 12x \) is:

For the hyperbola \( \frac{x^2}{25} - \frac{y^2}{9} = 1 \), find the coordinates of the foci.

Find the length of the latus rectum of the ellipse \( \frac{x^2}{36} + \frac{y^2}{25} = 1 \).

The equation of a parabola with vertex at origin and focus at (0, -3) is:

If the eccentricity of a hyperbola is \( \frac{5}{3} \) and the length of its transverse axis is 6, find the length of the conjugate axis.

A conic section is defined as the locus of points such that the ratio of the distance from a fixed point (focus) to the distance from a fixed line (directrix) is constant e. For e=0.5, the conic is: