# Calendar: 1878-1879 Page 591

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GENERAL LITERATURE AND SCIENCE 589 XIX tomrtrj ant nalgtttal eomttrg The rectangle contained by the diagonals of quadrilateral figure inscribed in circle is equal to both the rectangles con- tained by its opposite sides In the circle ABC the straight lines touching the circle st By Cy meet in prove that the chord of the circle parallel to ΑΒ which when produced passes through is bisected by AC In parabola prove that qr2 4sp pr and deduce the length of the chord of curvature drawn through the focus Two tangents are drawn to an ellipse from an external point prove that the angles which the tangents make with the respective focal distances of the point are equal Find the equation of the two tangents drawn from an external point to the ellipse cfi The equation of the circle passing through the centre of the ellipse and the points of contact of the tangents drawn from the point is Investigate the equation to the hyperbola referred to its asymptotes as axes From any point on one axis tangents are drawn to any hyper- bolas which have the axes for asymptotes prove that the points of contact lie on straight line parallel to the other axis Find the polar equation to conic the focus being the pole Find the condition that the general equation of the second degree may represent parabola two straight lines two coincident straight lines

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