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  Item Reference: KCLCAL-1898-1899-751

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FACULTY OF SCIENCE cxix fllflebratc &e01mtv1 YEARS II III 15 If Ο be the origin and 71 li two points whose relet- angular coordinates are xv y2 prove that the area of the triangle GAB is χ$2 22 If Ρ be point in triangle such that AP divides BC at in the ratio η and Ρ divides AD in the ratio 711 shew that ι η ABPC ACPA aAPB 16 Find the equation of any straight line in terms of the intercepts it makes on the axes The equations of the sides of parallelogram are 2y-3 2y-5 x-2y x-2y Find the lengths of the sides and the equations of the diagonals 17 Find the length of the perpendicular from on Ax By -f find also the equation of this perpen- dicular Two straight lines intersect at an angle of 60 Find the locus of point which moves 80 that the area of the quadri- lateral formed by the lines and the perpendiculars dropped on them from the point is constant 18 Shew that Ax2 Bxy Cy2 represents two straight lines Find the tangent of the angle between the two straight lines whose equation is J3x2 Uxy V3y2 Also find the equation of the pair of lines through the point Λ IS perpendicular to the above pair 19 Shew how to change the direction of rectangular axes without eh igirig the origin Also shew how to determine point to which if the origin be removed the terms of the first degree can be removed from an equation of the second degree Apply your method to 2x2 Sxy 17 46-0 18 20 Find the equation of the tangent at the point on the circumference of the circle x2 y2 β If does not lie on the circumFerence what is repre- genteel by the equation you find
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