| Isaac Todhunter - 1855 - 299 páginas
...from it on these n lines is constant ; find the conditions that the locus of P may be a circle. 31. **A point moves so that the sum of the squares of its distances from** the sides of a regular polygon is constant ; shew that the locus of the point is a circle. 32. A line... | |
| Isaac Todhunter - 1862
...moves so that the sum of the squares of io distances from the four sides of a square is constant ; shei **that the locus of the point is a circle. 12. A point...circle. 14. Shew what the equation to the circle becomes** wkc the origin is a point on the perimeter, and the axes are inclined at an angle of 120°, and the... | |
| Thomas Kimber - 1865 - 192 páginas
...the 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.... | |
| William Allen Whitworth - 1866 - 506 páginas
...right 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... | |
| W. P. TURNBULL, M.A. - 1867
...from two 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... | |
| 1869
...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... | |
| Philip Kelland - 1873
...given sphere : a point Q is taken in OP so that OP.OQ = k'. Prove that the locus of Q is a sphere. 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... | |
| Philip Kelland, Peter Guthrie Tait - 1873 - 227 páginas
...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... | |
| Rev. James White - 1878 - 148 páginas
...examples the base is taken as axis of x, and a perpendicular through its middle point as axis of y. **13. A point moves so that the sum of the squares of its distances from** the sides of a square, or from the angles of a square, are constant; shew that in both cases the loci... | |
| J. G - 1878 - 372 páginas
...from the four sides of a square is constant. Show that the locus of the point ii a circle. Ex. 12. **A point moves so that the sum of the squares of its distances from** the sides of an equilateral triangle is constant. Sliaw that the locus of the point it a circle. Ex.... | |
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