The Elements of Analytic Geometry
The Elements of Analytic Geometry
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In our eReader you can find the full English version of the book. Read The Elements of Analytic Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Elements of Analytic Geometry
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(6) * For the different manner in which the asymptotes are described when considered as conies belonging to the two different systems see 159, III.
117. ] CONIC SECTIONS. 177 Now, if h 2 > abj (4) and (6) are conjugate hyperbolas (116), while (5) represents their common asymptotes. Therefore (2) and (3) are the required equations.
COR. The lines represented by the equation are parallel to the asymptotes of the conic represented by the general equation (1).
EXAMPLES. Find the equations of the ta...ngent and normal to 1. Z 2 = 22/, at(-2, 2). 2. Y*=8x, at (2, 4).
3. X 2 + 2/ 2 =25, at (4, 3). 4. X 2 j/ 2 =16, at ( 5, 3).
5. Z' + 42/ 2 =8, at( 4, 3). 6. 2y* x*= 4, at (2, 2).
7. 2/ 2 + 4* + 22/ + l = 0, at(-4, 3).
8. 3z 2 + 5xy 2y*= 0, at (1, 3) and ( 2, 1).
9. 2z 2 4z2/ + 2/ 2 + 2s 4?/ 15 = 0, at (2, 3). 10. X 2 + 3x2/ + 4t/ 2 3z + 57/ + 9 = 0, at (4, 1).
Find the equations of the tangents to each of the following conies at the origin : 11. 2z 2 -|-32/ 2 +2z = 0. 12. Z 2 + 2z+32/ = 0.
13. 2xy + 5x 3y = 0.
What to read after The Elements of Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert L Albert Luther Candy to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(6) * For the different manner in which the asymptotes are described when considered as conies belonging to the two different systems see 159, III.
117. ] CONIC SECTIONS. 177 Now, if h 2 > abj (4) and (6) are conjugate hyperbolas (116), while (5) represents their common asymptotes. Therefore (2) and (3) are the required equations.
COR. The lines represented by the equation are parallel to the asymptotes of the conic represented by the general equation (1).
EXAMPLES. Find the equations of the ta...ngent and normal to 1. Z 2 = 22/, at(-2, 2). 2. Y*=8x, at (2, 4).
3. X 2 + 2/ 2 =25, at (4, 3). 4. X 2 j/ 2 =16, at ( 5, 3).
5. Z' + 42/ 2 =8, at( 4, 3). 6. 2y* x*= 4, at (2, 2).
7. 2/ 2 + 4* + 22/ + l = 0, at(-4, 3).
8. 3z 2 + 5xy 2y*= 0, at (1, 3) and ( 2, 1).
9. 2z 2 4z2/ + 2/ 2 + 2s 4?/ 15 = 0, at (2, 3). 10. X 2 + 3x2/ + 4t/ 2 3z + 57/ + 9 = 0, at (4, 1).
Find the equations of the tangents to each of the following conies at the origin : 11. 2z 2 -|-32/ 2 +2z = 0. 12. Z 2 + 2z+32/ = 0.
13. 2xy + 5x 3y = 0.
What to read after The Elements of Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert L Albert Luther Candy to read onlineMoreLess
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