. Algebraic geometry; a new treatise on analytical conic sections . p;, when 60° is theangle between the axes. 9. Prove that the straight line 2x+y = 2a, touches the circle x^ + y^+xy = a?,and find the co-ordinates of its point of contact. 10. Find the equations of the tangents to the circle x^ + y^ + xy=a^ aXthe points where it cuts the axis of y. 11. Find the equation of the straight line which touches the circlex^ + y^ + xy-ix-5y=0a,tt\i6 origin. 12. Find the equation of the tangent to the circle x^ + y^ + 2xy aosa + 2gx + ify=0 at the origin, and the equation of the radius which passes thr
. Algebraic geometry; a new treatise on analytical conic sections . p;, when 60° is theangle between the axes. 9. Prove that the straight line 2x+y = 2a, touches the circle x^ + y^+xy = a?,and find the co-ordinates of its point of contact. 10. Find the equations of the tangents to the circle x^ + y^ + xy=a^ aXthe points where it cuts the axis of y. 11. Find the equation of the straight line which touches the circlex^ + y^ + xy-ix-5y=0a,tt\i6 origin. 12. Find the equation of the tangent to the circle x^ + y^ + 2xy aosa + 2gx + ify=0 at the origin, and the equation of the radius which passes through theorigin. POLAR EQUATION OF A CIRCLE. 118. The polar equation of a circle of radius a, whose centre is atthe origin, is r==a. This is evident from the fact that every point on the circum-ference of the circle is at a distance a from the ,G. H 114 POLAR EQUATION OF A CIRCLE. [chap. vii. 119. The equation of the tcmgeitt at the point (a, a) on the circler = a is a = r<iOs{d-a). Let Q be the point {a, a), and P(r, 6) any point on the tangentat Pig. 74 lPOQ, = l PCs - L QjOx =6-a;.. OQ = OPeos(0-a), a = rms{9-a) is the equation of the tangent at Q. 120. To find the polar equation of a circle of radius a whose cir-cumference passesO-^J throvgh the origin and whose centrelies in the initiallim. _ Let P(r, 6) be ^ any point on the circumference and DA the diameter through the origin. lOPA is a,rt. L; PiQ. 75. .. OP = DA cos 6, r = 2a cos 6 is the required equation.
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