Exercises for Homework 4

Date: 2015-10-07; view: 473.

4.11. Find radius and the coordinates of center of circumference:

a) b)

4.12. Find lengths of semi-axes, eccentricity, the coordinates of focuses, compose equations of directrices of an ellipse: a) b) .

4.13. Let an ellipse be given. Determine whether the point lies on the ellipse, inside or outside of it: a) b) .

4.14. An ellipse in a given system of coordinates has a canonic equation. Compose this equation if:

a) chord connecting two vertices of the ellipse has length 5 and is inclined to its big axis under angle .

c) focuses of the ellipse are the points , and the directrices are lines .

4.15. Find semi-axes, eccentricity, the coordinates of focuses, compose equations of directrices and asymptotes of the following hyperbola: a) b)

4.16. A hyperbola is given. Determine whether the point lies on the hyperbola, inside of one of its branches or between branches: a) b) .

4.17. A hyperbola in a given system of coordinates has a canonic equation. Compose this equation if: a) the length of the real axis is 1, and the point (1, 3) belongs to the hyperbola.

b) the length of the imaginary axis is 1, and the vertex of the hyperbola divides the segment between focuses in ratio 4 : 1.

4.18. Find the coordinates of focus and compose the equation of directrix of the following parabola:

a) b) .

4.19. A parabola in a given system of coordinates has a canonic equation. Compose this equation if the distance from focus to directrix is 12.

4.20. Determine the type of the following curve of the second order, compose its canonic equation and find the canonic system of coordinates:

a) ; b) .