The elements of plane analytic geometry. A text-book including numerous examples and applications, and especially designed for beginners (1903)
Briggs, George R. (George Russell), b. 1853, Bôcher, Maxime, 1867-1918 · New York, J. Wiley & sons; [etc., etc.] · leaf 141
ct ? 74* We will next find the equations of a tangent and a normal^o an ellipse at a point /\ of the curve. y In the figure, P^ T is the tangent, andP^ JV the normal.The coordinates of P^are x^ = O M^ andy,^M,P,. Using the same me-thod as in § 49, wehave, corresponding toequation (4) of that… … 134 ANALYTIC GEOMETRY. Taking the limit of this as ^ and /i both approach zero, wehave P X and I a^y^ ^^-y, =^ (5) The equation of the tangent is, therefore, /yx, , y-yx ^-^/-^-^i) • • (6) and of the normal ^ - ^1 = 1^ (^ - ^i) (7) Clearing (6) of fractions, and transposing, we haveb^ x^x ■\- a^j\…
Geometry, Analytic -- Plane
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