Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...in 0, and take OA = 0A'= a. Then A and A' are points on the curve. Why? Now between F and F' take any point K. With F as center and AK as radius, describe arcs; with F' as center and A'K as radius, describe arcs intersecting the former in P and P'. By interchanging radii, Q and Q' are found. These all lie on the curve because the sum of the focal distances of each is 2 a. After finding enough points we join them by a smooth curve. (2) Mechanically. Fix pins at F and F' and join them by a string of length 2 a. A pencil point P moved so as to keep the string stretched will trace the ellipse; for in all positions of P, we have PF + PF'= 2 a. i-l. yy±-1 "a2 "" 62 is the required equation. The normal is (y--Vi) = j (x--xi) The subtangent and subnormal are found by putting y = 0 in equations of the tangent and normal; viz., subtangent =--x, b2 subnormal =-x, as Note.--That the subtangent is a function of the abscissa and a. 128. Equation of tangent in terms of slope.--The abscissas of the points of intersection of the line y = mx + o (1) with $+i=i are determined by the equation a;2 (mx + cf _ 1,„. & + p 1 (3) 3. The tangent and normal to the ellipse at the end of the latus rectum first quadrant are y + ex--a = 0, ey--x + ae3 = 0. 4. For what value of k will the line x + y = k touch the ellipse x-+ t = 1? a2 + b2 5. A square is inscribed in an ellipse. Find length of its side. 2a6 Ans-VZTf 6. Tangents to the ellipse from (h, k) make an angle t. Prove, h2 + k2-a2-b2 tan = 2 Vd2 h? + o2 k2-a2 b2. 7. P is any point on the ellipse. Show that the locus of the center of the circle inscribed in A FPF' F, F' are foci is the ellipse (1-e) x2 + (1 + e) y2 = e a2 (1-e). 8. The locus of the mid-point of a normal is the ellipse 4Vx2 + 4a?y2 (1 + ...
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