"Hyperbola" Example Sentences
1. The equation of the hyperbola can be written in standard form.
2. The asymptotes of the hyperbola intersect at its center.
3. The foci of a hyperbola are always located inside the curve.
4. The eccentricity of a hyperbola is always greater than 1.
5. The hyperbola is a conic section that is formed by the intersection of a plane and a cone.
6. The distance between the foci of a hyperbola is always constant.
7. The vertices of a hyperbola are the points where the curve intersects its major axis.
8. The minor axis of a hyperbola is perpendicular to its major axis.
9. The directrix of a hyperbola is a line that is equidistant from the foci.
10. The hyperbola has two branches that extend infinitely in opposite directions.
11. The hyperbola is a non-circular and non-elliptical shape.
12. The hyperbola can be oriented vertically or horizontally.
13. The standard equation for a horizontal hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1.
14. The standard equation for a vertical hyperbola is (y-k)^2/a^2 - (x-h)^2/b^2 = 1.
15. The hyperbola is a commonly studied geometric shape in mathematics.
16. The hyperbola is used in many real-world applications, such as in satellite communication and astrophysics.
17. The hyperbola is a symmetrical shape with two distinct limbs.
18. The branches of a hyperbola can never touch or intersect.
19. The equations of the two branches of a hyperbola have opposite signs.
20. The equation of a hyperbola can be graphed on a coordinate plane.
21. The length of the major axis of a hyperbola is equal to the distance between its vertices.
22. The length of the minor axis of a hyperbola is equal to 2 times the distance between its foci.
23. The hyperbola is one of the four basic types of conic sections.
24. The hyperbola is named after the Greek word "hyperbole" which means "excess" or "exaggeration."
25. The hyperbola is often used in SAT math questions and other standardized tests.
26. The hyperbola can be used to solve problems in physics and engineering.
27. The hyperbola has several unique properties that make it an important shape in mathematics.
28. The hyperbola can be classified as either horizontal or vertical depending on the orientation of its axis.
29. The hyperbola has an asymptote, which is a line that the curve approaches but never touches.
30. The hyperbola has an infinite number of points, but only a finite number of them lie on the curve.
Common Phases
1. The
hyperbola is a conic section;
2. It is defined as the set of all points in a plane;
3. The difference between the distances to two fixed points, called the foci, is a constant;
4. As a result, the
hyperbola has two arms that extend to infinity;
5. The axis of symmetry is a line that passes through the foci and the center of the
hyperbola;
6. The transverse axis is the segment that intersects the two vertices of the
hyperbola;
7. The conjugate axis is perpendicular to the transverse axis and passes through the center of the
hyperbola;
8. The eccentricity is a measure of how "stretched out" a
hyperbola is, and is defined as the ratio of the distance between the foci to the length of the transverse axis.