Calendar: 1877-1878 Page 597

GENERAL LITERATURE AND SCIENCE 595 whose distance from given point αβ shall be equal to given length Show that when the points coincide αβ 6a aby Find the tangent of the angle between the two straight lines represented by the equation Af Bxy Cx" δ Prove that the straight lines drawn from the angles of triangle to the middle points of the opposite sides meet at point point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant show that the locus of the point is circle Find the equaiion to the tangent at any point of circle and show that from any external point two tangents can be drawn to circle Interpret tlie equations -f r2 4xy י ן rcos20see0 2a2 If the tangent to the parabola at any point Ρ intersect the directrix in the point Ζ then SZ will be at right angles to SP 10 If the normal at any point Ρ of parabola meet the axis in the point then N6 2AS Also if from GK be drawn at right angles to SP then PK AS 11 If Ρ Ν be an ordinate to the parabola at then PJV2 4AS AN AB and AC are two lines at right angles to each other From fixed point on AC CR is drawn parallel to AB On AR produced if necessary Ρ is taken fuch that the perpendicular Ρ Ν upon AB is equal to CR Prove that the curve traced out by Ρ is parabola 12 In the parabola if QF be an ordinate to the diameterPT7 then QV SP PV Show also that if two chords of parabola intersect the rectangles contained by their segments are in the ratio of the parameters of the diameters which bisect the chords ρ