Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 164
refore we shall havethe area of the ellipse = Ttab. Hence: Theorem X. The area of an ellipse is a mean propor-tional between the areas of the circles described on the majorand minor axes. Tangents and Normals to an Ellipse. 134. Problem. To find the equation of the tangent toan ellipse at a given… … V -,{x - X), ^ ^ X — X Since {x, y) and {x, y) are on the ellipse, we have^^y -I- ^^c = ab 0: (^0 and ay^ + ^V = ctb, therefore «(/ - y) + h\^ - ^) = whence y - ?/ b x. + x-jo - x « • ll + ?/ THE ELLIPSE. 149 Substituting in (a), we have, for the equation of the secant, y - y --^-fr^i^ - ^)- i»)…
Geometry, Analytic
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
