This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1862 edition. Excerpt: ...extremities will be a con ntric ellipse with semi-axes equal to aV(! + l) and bJ(r?+l). 26. Apply the equation to the tangent in Art. 171 to find ie locus of the intersection of tangents at the extremities of mjugate diameters. 27. If from a point (x', y') of an ellipse a chord be drawn Mallei to a ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1862 edition. Excerpt: ...extremities will be a con ntric ellipse with semi-axes equal to aV(! + l) and bJ(r?+l). 26. Apply the equation to the tangent in Art. 171 to find ie locus of the intersection of tangents at the extremities of mjugate diameters. 27. If from a point (x', y') of an ellipse a chord be drawn Mallei to a fixed line, shew that the length of this chord varies as"--, --22 where f, is the inclination of 6 cos p r tangent at (a;', y) to the axis, and a the inclination of the fia line to the axis. 28. If through any point P of an ellipse two chords P' PR, be drawn parallel to two fixed lines and making &np a and /3 respectively with the tangent at P, shew that the nt P2 cosec a: PR cosec /3 is constant. 29. A parabola is touched at the extremities of the lata rectum by an ellipse of given magnitude; find the Ian rectum of the parabola. 30. The perpendicular from the centre on a line joining ti ends of perpendicular diameters of an ellipse is of constai length. 31. Chords are drawn through the end of an axis of a ellipse; find the locus of their middle points. 32. Chords of an ellipse are drawn through any fii?. point; find the locus of their middle points. 33. Two focal chords are drawn in an ellipse at rigr. I angles to each other; find their position when the rectangfe contained by them has respectively its greatest and lea' value. 34. In an ellipse if PP' and Q Q' be focal chords at rigangles to each other l-e'_ 1-e2 1 1-1i an arv A m ' tort 37. Perpendiculars are drawn from P and D the exmities of any pair of conjugate diameters on the diameter = a; tan a; shew that the sum of the squares of the perpenulars is a2 sin2 a + b cos2 a. 38. The excentric angles of two points P and Q are j, and respectively; shew that the area of the...
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