Calendar: 1881-1882 Page 631

632 GENERAL LITERATURE AND SCIENCE Find the length of the perpendicular δ From hkl on the line Ax By Cz Explain fully the convention as to sign of the radical which occurs in the results Find the equation to circle referred to two tangents inclined at an angle ω as axes If be the length of the tangents show that the angle φ between the lines joining the origin to the points in which the line χ -f- cuts the circle is given by ω sin2 tan φ 2cos Kf a1 cos ω Find the polar equation to the parabola referred to its focus as pole Show that one fo irth of the latus-rectum is an harmonic mean between the segments of any focal chord Prove the more general case oi this theorem namely if r19 r2 יי be η radii vectores drawn equally inclined to each other rx r2 r3 rn Define the eccentric angle of point on an ellipse Find the equation to the tangent to an ellipse in terms of the eccentric angle of the point of contact If χ be points on an ellipse and η any integer show that are also points on the ellipse Find the equation to the hyperbola referred to its asymp- totes as axes system of parabolas is drawn touching the asymptotes of rectangular hyperbola at the extremities of their latera recta Show that the product of the perpendiculars let fall from the points of intersection of the hyperbola and