Calendar: 1870-1871 Page 514

514 GENERAL LITERATURE AND SCIENCE Show how to convert an equation in rectangular coordinates into homogeneous equation in trilinear coordinates Interpret the result when the equation to line presents itself in the form Three straight lines drawn from the vertices of triangle divide the opposite sides in the ratios tii and η show that these lines meet in point State and prove the harmonic properties of complete quadrilateral Find the length of the tangents from the point to the circle x2 y1 a2 and changing its sign give geometrical meaning to the result when Λ it lies within the circle 10 Find the locus of the point from which tangents of equal length can be drawn to two given circles Give construction for the line Apply the method by which the radical axes of three circles are proved to pass through common point to show that the three perpendiculars from the middle points of the sides of triangle do so 11 Find the condition that the straight line mx -f may touch the circle x2 y2 Φ Show analytically that the locus of intersection of pairs of tangents to circle at right angles to each other is concentric circle 12 Explain the position and properties of the line hx ley a2when hk lies upon the circle x2 -y2 a2 without the circumference within Assuming its property in the first case prove those in the latter cases 13 Find the equation to the pair of tangents from the origin to the circle af r2 and show that the chord of contact is the line ax by a2 b2 r2 14 Show that -f- "passes through the value as χ passes through zero ax- Find the limit of-ז when χ 15 Define the differential coefficient of function with respect to variable and obtain from' first principles the differential