1 Definition: An ellipse is the set of all points in a plane such that the sum of the distances from P to two fixed points (F1 and F2) called foci is constant. 9.4 Ellipse 2 A few terms: 1.Major axis: 2. Minor axis: 3. Vertices: 4.Co-vertices: 5. Foci: 6. Center: Longer axis of the ellipse Shorter axis of the ellipse Endpoints of the Major axis (a’s) Endpoints of the Minor axis (b’s) Always on the Major axis (c’s) Where the Major and Minor intersect (h,k) 3 Ellipses can have either a horizontal major axis or a vertical major axis. Horizontal Major Axis Vertical Major Axis Note: When the bigger number is under the x term, the major axis will be on the x- axis (or parallel to it if translated). When the bigger number is under the y term, the major axis will be on the y-axis (or parallel to it if translated). Center (h, k) 4 -The length of the major axis is _______ -The length of the minor axis is ________ -The foci are always on the __________ axis. - The following are ___________ true for ellipses: a: b: c: 5 To write an equation you need the CENTER and the a’s and b’s. Example 1: Write the standard form equation for an ellipse with foci of (0, -4) and (0, 4) and with minor axis of 6. 6 To write an equation you need the CENTER and the a’s and b’s. Example 2: Write the standard form equation for an ellipse with foci of (-8, 0) and (8,0) and with major axis of 20. 7 Example 3: Find the vertices and co-vertices. Is the major axis vertical or horizontal? 8 Example 4: Put the following equations in standard form for an ellipse. State the vertices, co-vertices, and foci. Does the ellipse have a horizontal or vertical major axis? 9 Example 5: Sketch. Label the center, foci, vertices and co-vertices. 10 Example 6: Write the standard equation for an ellipse with the given characteristics. a. Foci: (5,0) and (-5, 0 )b. Co-vertices: (0,2) and (0, -2) Vertices: (9, 0) and (-9, 0) Vertices: (3,0) and (-3, 0) 11 Example 7: Write a standard form equation for each ellipse. Identify the center, foci, vertices, and co-vertices. 12 13
center of an ellipse the midpoint of both the major and minor axes conic section any shape resulting from the intersection of a right circular cone with a plane ellipse the set of all points [latex]\left(x,y\right)[/latex] in a plane such that the sum of their distances from two fixed points is a constant foci plural of focus focus (of an ellipse) one of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point [latex]\left(x,y\right)[/latex] on the ellipse is a constant major axis the longer of the two axes of an ellipse minor axis the shorter of the two axes of an ellipse Contribute!Did you have an idea for improving this content? We’d love your input. Improve this pageLearn More Indian Navy SSR Agniveer Results Released! The Indian Navy had released the official notification for the Indian Navy SSR Agniveer Exam 2022. A total of 2800 vacancies are released for the recruitment process of Indian Navy SSR AA. The application process has started on 1st July and candidates can apply till 27th July 2022. The selection process includes a Written Test, Physical Fitness Test (PFT), and Medical Examination. With a salary of Rs. 30,000, it is a golden opportunity for job seekers.
Dear student, A hyperbola is "the set of all points in a plane such that the difference of the distances from two fixed points (foci) is constant". The difference of the distances to any point on the hyperbola (x,y) from the two foci (c,0) and (-c,0) is a constant. That constant will be 2a. Regards. |