Practice problems of the ellipse
Number of problems found: 5
- Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane.
- Circle in rhombus
In the rhombus is an inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
- Tangents to ellipse
Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1].
- Find the 15
Find the tangent line of the ellipse 9 x² + 16 y² = 144 that has the slope k = -1