Calendar: 1873-1874 Page 621

THE SCHOOL 621 Find the equation to the tangent at the point of the circle- 2ע c2 Determine also the equation to the chord of contact of tangents drawn from an external point 10 Trace the points or curves represented by the equa- tions y2 ax x2 ay 4ax ay a2 4a 11 Investigate the condition that the line- χ cos β sin θ ρ may be tangent to the ellipse X- Find the locus of the point of intersection of tangents to an ellipse at right angles to each other 12 Trace the curve x2 y2 c2 and find the equations to its asympotes What does this equation become if the axis be turned through 45 13 Prove that the polar equation of conic the focus being the pole and the latus rectum is- cos Θ τ Show that the equation to the tangent at the point Θ is- cos θ' cos θ' θ τ and determine the equation to the normal at the same point 14 Prove that the equation- י represents parabola touching the co-ordinate axes and find the co-ordinates of its focus and the equation to its directrix