| Isaac Todhunter - 1855 - 299 páginas
...inversely as the latus rectum ; find the locus of these points. 21. Two conic sections have a common focus **S through which any radius vector is drawn meeting...lines are inversely proportional to the corresponding** excentrities. 22. A line is drawn cutting an ellipse in the points P, p • let Q be either of the... | |
| 1855 - 299 páginas
...as the latus rectum ; find the locus of these points. 21. Two conic sections have a common focus 8 **through which any radius vector is drawn meeting the...lines are inversely proportional to the corresponding** excentrities. 22. A line is drawn cutting an ellipse in the points P, p . let Q be either of the points... | |
| Norman Macleod Ferrers - 1861 - 184 páginas
...which give the focus in that case. EXAMPLES. 1. HAVING given a focus and two points of a conic section, **prove that the locus of the point of intersection of the tangents at** these points will be two straight lines, passing through the focus, and at right angles to each other.... | |
| Isaac Todhunter - 1862
...inversely as the latus rectum ; find the locus of these points. 21. Two conic sections have a common focus **S through which any radius vector is drawn meeting...directrices of the conic sections, and that the sines** 01 the angles which it makes with these lines are inversely proportional to the corresponding excentricities.... | |
| Robert Henry Wright - 1865 - 128 páginas
...directed to that infinitely distant point. 298. A focus and two points of a conic section being given, **prove that the locus of the point of intersection of the tangents at** these points will be two straight lines passing through the focus and at right angles to each other.... | |
| Joseph Wolstenholme - 1867 - 344 páginas
...intersect in A, B, C, D • through D is drawn a straight line to meet the curves again in two points ; **prove that the locus of the point of intersection of the tangents at** these points is a curve of the fourth degree and third class, having cusps at A, B, C, and touching... | |
| Charles Smith - 1883 - 352 páginas
...parabola make angles with the axis such that the product of the tangents of their halves is constant; **prove that the locus of the point of intersection of the tangents** is a confocal parabola, 50. If the circle described on the chord PQ of a parabola as diameter cut the... | |
| ...at A and B. Through a given point C on AB a variable straight line is drawn, cutting OA, OB in P and **Q respectively. Prove that the locus of the point of intersection of the** other tangents from P and Q is a straight line through 0. [CS] 10. A conic touches the sides QR, RP,... | |
| ...ellipse 3x2 + 4?/2 = 28 whose mid-point is the point (1, 1). Find also the length of this chord. 10. **Prove that the locus of the point of intersection of the tangents at** the ends of conjugate diameters of the ellipse a;2/a2 + 2/2/62 = 1 is the ellipse x2/a2 + i/2/62 =... | |
| Jain, P.K. - 1986 - 362 páginas
...the chord. Prove that the locus of the point of intersection of the normals is another parabola. 20. **Prove that the locus of the point of intersection of the tangents** to the parabola is a line parallel to j-axis. 21. If a chord of the parabola y"=4ax subtends a right... | |
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