...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...

...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....

...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...

...three fixed points. In what case does the conic degenerate into two intersecting straight lines ? 45. Find the locus of a point which moves so that the sum of the squares on the tangents drawn from it to the ellipse, -—- - + —jf = 1, is constant. X a v'...

...of the perpendiculars from any other point P, will bisect OP. [Such a polygon has the property that the locus of a point, which moves so that the sum of the squares on its distances from the sides is constant, is a circle.] 2254. The limiting position...

...equidistant from three given straight lines. 9. Inscribe a regular pentagon in a given circle. 10. Find the locus of a point which moves so that the sum of the squares of its distances from four given points is constant. What is the least possible value of...

...at the points, and a, b are the semi-axes of the ellipse. 32. Two equal circles touch one another, find the locus of a point which moves so that the sum of the tangents from it to the two circles is constant. 33. Prove that the sum of the products of the...

...locus of a point, whose distances from two given planes are in a constant ratio, is a plane. Ex. 10. The locus of a point, which moves so that the sum of its distances from any number of fixed planes is constant, is a plane. 21. The co-ordinates of any point on the line of...

...locus of a point, whose distances from two given planes are in a constant ratio, is a plane. Ex. 10. The locus of a point, which moves so that the sum of its distances from any number of fixed planes is constant, is a plane. 21. The co-ordinates of any point on the line of...

...(o, -2^-) to the circle ж2 + ?/2=25. Find the length of the chord joining the points of contact. 16. Find the locus of a point which moves so that the sum of the squares of its distances from the four sides of a square is constant. 17. A point inoves so that...