# Calendar: 1889-1890 Page 759

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ENGINEERING DEPARTMENT 113 If be the fixed point SO perpendicular to the fixed straight line and the locus cut OS internally and externally in prove that Ο OA1 OS" Write down the most general equation of circle and show how it may be reduced to its simplest form Apply your method to x1 -f Ax 8y Fiml the coordinates of the points where it cuts the axes and draw the figure Prove that the straight line mx is tangent to η yl ax and find the coordinates of the point of contact If ar x2 are the abscissae 01' points of which the tangents are at right angles prove that xx x2 a1 Prove that the normal to the ellipse τ at the point for which χ cos φ sin φ is ax sec φ iycosec a1 Ul Find the coordinates of the foot of the perpendicular from the origin on this line Draw figure for each of the following 77 2f ii ax iii αοο&θ iv rsin0 Explain the meaning of the process called Integration and state briefly the sort of problems in which it is employed Find the indefinite integrals of the following Ρ a2 8111 aj χλ an deduce fhr a2 dx sinaxdx r2-4 Vx -x fdx "a Λ curve is such that the tangent of the angle which the tangent at any point mak es with the axis of χ varies as the product of the abscissa and ordinate of the point Find its equation Given that the angle in question is obtuse when χ and are positive draw the figure

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