Calendar: 1873-1874 Page 620

620 THE SCHOOL 15 Define the evolute of curve and find the equation to the evolute of the curve x2 ay Conic rrttons Define conic section and describe the relative positions of the focus and directrix 1st when the conic is circle 2ndly when it consists of two straight lines Describe method of constructing parabola mechani- cally Find the locus of the centre of circle touching given straight line and given circle Prove that the tangent at any point of an ellipse is equally inclined to the focal distances of that point and that the two tangents drawn from any external point are equally inclined to the focal distances of the external point Find the locus of the centre of circle touching two given circles taking only into consideration the case in which the two given circles are external to each other If the tangent at any point Ρ of an ellipse meet the axis in and Ρ Ν he the ordinate and the centre prove that- CN CT C2 Show how to cut from given cone 1st parabola 2ndly when possible rectangular hyperbola If χ and be the rectangular co ordinates of point find the loci of the equations- y2 xy י Explain what are meant by the polar co-ordinates of point and find the polar equation to straight line in the form- ρ cos β If triangle ABC remain similar to given triangle and if the point be fixed and the point Ρ move along given straight line find the locus of the point