Question

PROVE THAT THE ENDS OF THE EQUI-CNJUGATE DIAMETERS OF A SERIES OF CONFOCAL ELLIPSESARE ON A CONFOCAL RECTANGULAR HYPERBOLA​

Answer 1

Answer:

54. If PB be drawn parallel to an asymptote, to meet the

conjugate hyperbola in i>, CP and CB are conjugate diameters.

Examples. 127

55. If QR be a chord parallel to the tangent at P, and if

QLy PNf RM be drawn parallel to one asymptote to meet the

oiher,

CL . CM= CN\

56. If a circle touch the transverse axis at a focus, and pass

through one end of the conjugate, the chord intercepted by the

conjugate is a third proportional to the conjugate and transverse

semi-axes,

57. A line through one of the vertices, terminated by two

lines drawn through the other vertex parallel to the asymptotes,

is bisected at the other point where it cuts the curve.

58. If PSQ be a focal chord, and if the tangents at P and Q