 | Michel Chasles - Cone - 1837 - 564 pages
...а2е? cos2 ф. Hence CW2 = CQ2 + CQ'2 = a2 + a2 (l - e2) = a2 + 62, and therefore the locus of the intersection of two tangents to an ellipse at right angles to one another is a circle whose center is С and radius equal to v a2 + W. The Ellipse referred to its conjugate Diameters. 138.... | |
 | John Hymers - Conic sections - 1837 - 486 pages
...CQ'2 = o8 - a* Hence CW* = CQ2 + CQ'2 = a» + a8 (l - e8) = a2 + 6», and therefore the locus of the intersection of two tangents to an ellipse at right angles to one another is a circle whose center is С and radius equal to ^/a* + b3. The Ellipse referred to its conjugate Diameters.... | |
 | John Hunter (of Uxbridge.) - 1866 - 104 pages
...that is, -=cos 0 ; Ar C^jl a PM OP or -,=6 which is the equation to an ellipse. Ex. (6). Determine the locus of the point of intersection of two tangents to an ellipse at right angles to each other. The equation to the tangent is if the tangent pass through a given point, (Ji, fc), then... | |
 | James Maurice Wilson - 1872 - 160 pages
...a parabola. Hence obtain the tangent property of the parabola. 41. The locus of the intersection of tangents to an ellipse at right angles to one another is a circle. Deduce the corresponding property in the parabola. 42. The semi-latus rectum is a harmonic mean between... | |
 | Charles Smith - Conic sections - 1883 - 388 pages
...then will the polar of Q pass through P. This may be proved exactly as in Art. 78. 1 20. To find the locus of the point of intersection of two tangents to an ellipse which are at right angles to one another. The line Whose equation is y = mx + Ja'm' + 63 ................... | |
 | John Hunter - Conic sections - 1885 - 130 pages
...triangles, -- =3L_ , that is, -=cos 0; or which is the equation to an ellipse. Ex. (6). Determine the locus of the point of intersection of two tangents to an ellipse at right angles to each other. The equation to the tangent is y— mx= + if the tangent pass through a given point, (h,... | |
 | James Maurice Wilson - Conic sections - 1885 - 180 pages
...a parabola. Hence obtain the tangent property of the parabola. 41. The locus of the intersection of tangents to an ellipse at right angles to one another is a circle. Deduce the corresponding property in the parabola. 42. The semi-latus rectum is a harmonic mean between... | |
 | Luigi Cremona - Geometry, Projective - 1885 - 434 pages
...equal to OT2 — OA2. Thus OT2 = OA2 ± OB2 - constant, so that we have the following theorem * : The locus of the point of intersection of two tangents to an ellipse or a hyperbola which cut at right angles is a concentric circle. This circle is called the director... | |
 | Kansas Academy of Science. Meeting - Science - 1896 - 440 pages
...origin and the points of contact of "central " tangent circles from the point to the oval.] 1. The locus of the point of intersection of two tangents to an ellipse, which are at right angles to one another, is the director circle of radius equal to (a1 + 61)* when... | |
 | Kansas Academy of Science. Meeting - Science - 1896 - 388 pages
...the origin and the points of contact of "central" tangent circles from the point to the oval.] 1. The locus of the point of intersection of two tangents to an ellipse, which are at right angles to one another, is the director circle of radius equal to (a- -\- b1)^ when... | |
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To find the locus of the point of intersection of two tangents to an ellipse which are at right angles to one another. The line Whose equation is y = mx + Ja'm' + 63 ................ (i) will touch the ellipse, whatever the value of m may be. 
