![the definition of a parabola abscissa the definition of a parabola abscissa](https://media.cheggcdn.com/study/8ad/8add1e84-31c0-417b-a54f-89920b96defe/DC-317V1.png)
Find coordinates of tricks.ĭividing both sides of the equation by 580, we get The desired equation will be the equation The second equation to determine a 2 and b 2 gives the ratioįind a 2 =16, b 2 = 9. Let us write the canonical equation of the hyperbolaīy condition, the point M (-5 9/4) belongs to the hyperbola, therefore, M (-5 9/4) if the focal length of the hyperbola is 10. Write canonical equation hyperbola passing through a point So, extraneous points could appear only under the condition 0 At X >Ī right part equation (4) is positive, since The left side of equation (4) is also always non-negative. Both parts of equation (3) are obviously non-negative for all values X and at. (3) and (4) did not violate the equivalence of the equations. Let's square both sides of the resulting equality:Īfter appropriate simplifications and transformations:Įquation (6) is called the canonical equation of the hyperbola.Ĭomment. Denoting it through 2 a, we getĠ, then equation (2) can be written without the modulus sign as follows:
![the definition of a parabola abscissa the definition of a parabola abscissa](https://g4itec5aee10a.weebly.com/uploads/2/6/0/2/26026936/2016855.png)
112), then, by definition of a hyperbola, the modulus of the difference | F 1 M | - | F 2 M | constant. These points are called tricks hyperbolas, and the distance between them is focal distance.ĭenote the foci of the hyperbola by the letters F 1 and F 2. Hyperbole is called a set plane points, for each of which the modulus of the difference in distances to two given points of the plane is constant and less distance between these points.