Practice problems of the ellipseDirection: Solve each problem carefully and show your solution in each item.
Number of problems found: 7
- Artificial 57081
Determine the average speed and orbit of the Earth's first artificial satellite. Its distance from the Earth's surface in the perigee was 226 km, and in the apogee, 947 km.
- 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.
- Coordinate 82580
Write the equation of the ellipse that passes through the points and its axes are identical to the coordinate axes, when: A = [2, 3] and B = [−1, −4].
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the ellipse's center.
- Find the 15
Find the tangent line of the ellipse 9x² + 16y² = 144 that has the slope k = -1
- 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].
- Circle in rhombus
In the rhombus is an inscribed circle. Contact points of touch divide the sides into parts of length 14 mm and 9 mm. Calculate the circle area.