Elements of Analytical Geometry
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In our eReader you can find the full English version of the book. Read Elements of Analytical 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 Elements of Analytical Geometry
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To draw a tangent from a point without the curve, as N. Join the point with the focus ; with this distance as a radius, and the given point as a centre, describe an arc cutting the direc- trix in the points C and C ; through these points, draw lines par- allel to the axis, cutting the curve in the points M and M' ; join these points with the given point and we shall have the tangents NM and NM'. For, since MF MC, and NF = NC, the line NM has two of its points equally distant from the points F a...nd C, is therefore perpendicular to FC at its middle point and bisects the angle FMC.
Let the co-ordinates of the given point N", be denoted by x' and y'. Since this point is on the tangent, we must have the equation of condition, Art. (23), y'y" = p(x' + a*")-* (1).
and since the point of contact is on the parabola, we also have the equation of condition, y" % — 2px".
INDETERMINATE GEOMETRY, 113 In these equations x" and y" are unknown, and since one is of the first and the other of the second degree, their combination will give an equation of the second degree, and there will be two values of x" and two corresponding of y".
What to read after Elements of Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert E Albert Ensign Church to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
To draw a tangent from a point without the curve, as N. Join the point with the focus ; with this distance as a radius, and the given point as a centre, describe an arc cutting the direc- trix in the points C and C ; through these points, draw lines par- allel to the axis, cutting the curve in the points M and M' ; join these points with the given point and we shall have the tangents NM and NM'. For, since MF MC, and NF = NC, the line NM has two of its points equally distant from the points F a...nd C, is therefore perpendicular to FC at its middle point and bisects the angle FMC.
Let the co-ordinates of the given point N", be denoted by x' and y'. Since this point is on the tangent, we must have the equation of condition, Art. (23), y'y" = p(x' + a*")-* (1).
and since the point of contact is on the parabola, we also have the equation of condition, y" % — 2px".
INDETERMINATE GEOMETRY, 113 In these equations x" and y" are unknown, and since one is of the first and the other of the second degree, their combination will give an equation of the second degree, and there will be two values of x" and two corresponding of y".
What to read after Elements of Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert E Albert Ensign Church to read onlineMoreLess
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