...of an equilateral triangle is constant ; shew that the locus of the point is a circle. 13. A point moves so that the sum of the squares of its distances from any given number of fixed points is constant ; shew that the locus is a circle. 14. Shew what the equation...

...of an equilateral triangle is constant ; shew that the locus of the point is a circle. 13. A point moves so that the sum of the squares of its distances from any given number of fixed points is constant ; shew that the locus is a circle. 14. Shew what the equation...

...radius of which is equal to a. Interpret each of the equations я? + y* = 0 and x* — y* = 0. A point moves so that the sum of the squares of its distances from the three angles of a triangle is constant. Prove that it moves along the circumference of a circle. 15. Investigate...

...lines, the polar of any point whatever passes through the intersection of the right lines. (148) A point moves so that the sum of the squares of its distances from n given straight lines is constant. Shew that it will describe a conic section. (149) If all but one...

...other points # 3 y 3 , x 4 y 4 . Prove that the locus of the point is the straight line 32. A point moves so that the sum of the squares of its distances from n given points = the sum of the squares of its distances from n other given points. Find the locus...

...that the locus of P is a circle, find geometrically the circle's position and magnitude. 21. A point moves so that the sum of the squares of its distances from any number of given points is constant. Prove that the locus of this point is a circle. 22. Find the...

...whole line. 5. Given the base, area, and one of the angles at the base, construct the triangle. 6. Find the locus of a point which moves so that the sum of the squares of its distance from four given points is constant. On the Quadrature of a Rectilineal Area. There is one...

...middle points of opposite sides intersect in the line which joins the middle point of the diagonals. 77. The locus of a point which moves so that the sum of the squares of its distances from three given points is constant is a circle. BOOK II. THE CIRCLE. INTRODUCTION. Def. 1. IF a point moves...

...given point parallel to a given plane ? parallel to a given line ? in. ANALYTIC GEOMETRY. 1. Determine the locus of a point which moves so that the sum of the Hquares of its distances from two fixed points is constant. Also determine the locus, changing sum...

...constant. Prove that its locus is either a plane or a. sphere. EX. 11.] ADDITIONAL EXAMPLES. 89 11. A point moves so that the sum of the squares of its distances from a number of given points is constant. Prove that its locus is a sphere. 12. A sphere touches each of...