Calendar: 1884-1885 Page 637

GENERAL LITERATURE AND SCIENCE 631 base shall have the same ratio which the other sides of the triangle have to one another The straight lines which bisect the angles of triangle meet at the same point 10 Similar triangles are to one another in the duplicate ratio of their homologous sides 11 Express the area of triangle in terms of the coordin- ates of its angular points Find the area of the triangle contained by the axis of and the straight lines χ cX1 m2 c2 12 Find the angle between two given straight lines Take as an example the Hues whose equations are 2y 13 Find the length of the perpendicular drawn from given point upon given straight line Find the distance of the point of intersection of the lines 2x Sy 3x 4y from the line 2x 14 Determine when the general equation of the second degree ax2 bxy cy2 dx ey represents two straight lines Show that 2y2 xy x2 &0 מ represents two straight lines at right angles to one another 15 Interpret the equation x2 y2 Ax By point moves so that the sum of the squares of its dis- tances from the sides of an equilateral triangle is constant show that the locus of the point is circle 16 Find the equation to the tangent at any point of circle If the line is tangent to the circle x2 -y2 c29 find the relation betwreen and 17 Find the equation to the parabola point moves so that its shortest distance from given circle is equal to its distance from given fixed diameter of that circle find the locus of the point 18 Find the equation to the tangent at any point of parabola in terms of the tangent of the angle which the straight line makes with the axis of the parabola