Show that, for the ellipse (x2 / a2 )+ (y2 / b2 ) = 1, the product of the perpendicular distances between the foci and any tangent to the ellipse is the square of the...

The equation 4x^2+9y^2-36y = 0 defines a shifted ellipse. Write this equation in the standard form, find the center, focus, vertices of this ellipse, the lengths of major and minor axes and sketch...

Write equation in standard form. Cirles, identify the center and radius. Identify ellipses and hyperbole identify the center.

Circles, ellipses, and hyperbolas identify the center. Write equation in standard form.

Identify the conic that this polar equation represents. Also, give the position of the directix. r=1/(1+costheta) The equation defines a circle. The equation defines an ellipse...

Find a polar equation for this conic. A focus is at the pole. e = 6; directrix is parallel to the polar axis 2 units below the pole r=12/(1+6costheta) r=12/(1-6costheta)...

Identify the conic that this polar equation represents. Also, give the position of the directix. r=3/(4-2costheta) The equation defines a circle. The equation defines a parabola....

Identify the conic that this polar equation represents. Also, give the position of the directix. r=4/(2-3sintheta) The equation defines an ellipse. The equation defines a parabola...

Identify this equation without completing the square. x2 + y2 - 8x + 4y = 0 The equation defines a circle. The equation defines an ellipse. The equation defines a hyperbola...