Calendar: 1880-1881 Page 635

GENERAL LITERATURE AND SCIENCE 635 15 Show that the polar reciprocal of circle is conic section of which the origin is the focus and which is an ellipse hyperbola or parabola as the origin is inside outside or on the circle Keciprocate if from any point on the circumference of circle perpendiculars are drawn to the sides of an inscribed triangle their feet will lie in straight line 16 If ax2 2hxy bf 2yx 2fy represent hyperbola show that ah h2 ax2 2hxy by2 2gx 2fy af2 bg2 2fgh is the equation of the conjugate hyperbola 17 Find the length of the perpendicular from the point fgh on the straight line χ ζ η ך Find the general equation to right cone whose vertex is abc and axis is χ ζ η XVI -aigrtra an Cfjwrji of £quatton£i Assuming the Binomial Theorem to be true when the index is positive integer shew that it is true generally Find the coefficient of in the expansion of and prove that -y2 5' xY ηχη -f χ η-2 If ad inf 4- 5a3 271 3x be expanded in series ascending by powers of find the coefficient of xn