Mathematics for Agricultural Students (Paperback)

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. 1914 Excerpt: ...point T upon the shorter axis of the ellipse produced. This fact will be made use of in drawing the tangent to an ellipse. Let ABA'B', Fig. 53, be an ellipse to which a tangent line is to be drawn at the point P. Draw the circle with B'B as diameter. From P drop a perpendicular upon B'B cutting the circle at Q. 1 It can be shown that the section of a right circular cone made by a plane cutting all of its elements on the same side of the vertex is an ellipse. Through Q draw QT tangent to the circle (perpendicular to OQ). Draw TP, which will be tangent to the ellipse at the point P. It is left for the student to show that the above statement is correct. We shall now show how to draw a tangent to an ellipse through a point S, not upon the curve. Let S, Fig. 47, be a point in the plane of the ellipse, through which the tangent line is to be drawn. Draw SS' parallel to PQ, intersecting the plane OCQ at S'. Draw SK and S'K perpendicular to BB' From the similar right triangles SS'K and AGO it follows that: S'KjSK = CO I AO Let ABA'B', Fig. 54, be the ellipse to which the tangent is to be drawn from the point S. Draw ASW. Draw CW. Draw SK perpendicular to BOW, cutting CW at the point S'. From S' draw the two tangents to the circle BCB'D. Let Q3 and Q2 be the points of tangency. Draw R1Q1P1 and R2Q2P2 perpendicular to B'OB cutting the ellipse in the points P3 and P2. Draw PiS and P2S. PiS and P-S are the tangents to the ellipse drawn from the points S. PiS and QiS' intersect upon B'BW; and P2S and Q2S' intersect upon B'BW. It is left for the student to show that the above statements are correct. Exercises 1. Find the value of each semi-axis, the focal distance, and the eccentricity for each of the following: (a) j ] f = 1-(c) 100x + 4y = 400. (b) + = L 7...