A Treatise On Plane Co Ordinate Geometry As Applied to the Straight Line And T
A Treatise On Plane Co Ordinate Geometry As Applied to the Straight Line And T
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In our eReader you can find the full English version of the book. Read A Treatise On Plane Co Ordinate Geometry As Applied to the Straight Line And T 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 A Treatise On Plane Co Ordinate Geometry As Applied to the Straight Line And T
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93, 94, that the tangent at any point of an ellipse meets it at only one point, and that NOEMAL TO AN ELLIPSE. 153 a straight line wliich meets an ellipse at only one point is the tangent at that point.
172. The tangents at the extremities of either axis are parallel to the other axis.
For the co-ordinates of A are a, 0. (See the figure to Art. 162. ) Hence, putting x = a, and 2/'=0, the equation c^yy + Vxx — c^W" becomes x — a, which is the equation to a straight line through A parallel to OYi... Similarly the tan- gent at A is parallel to (7F, and the tangents at B and B are parallel to CX.
173. To find the equation to the normal at any point of an ellipse, (See Definition, Art. 97. ) Let x\ y be the co-ordinates of the point ; the equation to the tangent at that point is 2/ = --x^a; + - (1).
The equation to the straight line through [x', y') at right angles to (1) is 2'-2''=S^(^-^') (2).
This is the equation to the normal at {x\ y).
174. The equation to the normal may also be expressed in terms of the tangent of the angle -which the straight line makes with the major axis of the ellipse.
What to read after A Treatise On Plane Co Ordinate Geometry As Applied to the Straight Line And T?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
93, 94, that the tangent at any point of an ellipse meets it at only one point, and that NOEMAL TO AN ELLIPSE. 153 a straight line wliich meets an ellipse at only one point is the tangent at that point.
172. The tangents at the extremities of either axis are parallel to the other axis.
For the co-ordinates of A are a, 0. (See the figure to Art. 162. ) Hence, putting x = a, and 2/'=0, the equation c^yy + Vxx — c^W" becomes x — a, which is the equation to a straight line through A parallel to OYi... Similarly the tan- gent at A is parallel to (7F, and the tangents at B and B are parallel to CX.
173. To find the equation to the normal at any point of an ellipse, (See Definition, Art. 97. ) Let x\ y be the co-ordinates of the point ; the equation to the tangent at that point is 2/ = --x^a; + - (1).
The equation to the straight line through [x', y') at right angles to (1) is 2'-2''=S^(^-^') (2).
This is the equation to the normal at {x\ y).
174. The equation to the normal may also be expressed in terms of the tangent of the angle -which the straight line makes with the major axis of the ellipse.
What to read after A Treatise On Plane Co Ordinate Geometry As Applied to the Straight Line And T?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
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