...being given in position, and also a point R, (fig. 11,) to find a point D in one of the given lines AB, such, that the sum of the squares of the perpendiculars drawn from D to the other two lines, should have a given ratio to the square of DR, it is plain, that the finding...

...referred to its axes, and Q being the angle AGP. If an ordinate to P meet Q Q' in R, the locus of Л is an ellipse. 16. The locus of a point such that...the side opposite to the angle A in D, then CD : BD :: 5' : c\ 17. With the notation of Art. 313, shew that the equation to the line through С and the...

...axes, and 0 being the angle AGP. If an ordinate to P meet Q Q' in R, the locus of H is an ellipse. 1 6. The locus of a point such that the sum of the squares...touch the side opposite to the angle A in D, then CD : ED :: V : c2. 17. With the notation of Art. 313, shew that the equation to the line through C and...

...three planes intersect each other at right angles, so that the planes pass through a fixed point ; find the locus of a point, such that the sum of the squares on its distances from the three planes may be constant for all points in the locus. 74. Describe a...

...triangle ABC. 40. Find the locus of the vertices of triangles of equal area upon the same base. 41. Find the locus of a point, such that the sum of the squares on its distances from two given points is equal to the square on the distance between the two points....

...a circle is seen from a point is the angle contained by the two tangents from that point. 186. Find the locus of a point, such that the sum of the squares of its distances from the vertices of a given triangle is equal to the square of a given line. (Ex. 166.)...

...tan A = tan B = tan C; hence A = B = С = 6o" ; and therefore the triangle is equilateral. 2. Find a point such that the sum of the squares of the perpendiculars...from it to the sides of a given triangle shall be a minimum. Let x, y, z denote the perpendiculars : a, b, c, the sides of the triangle, then « = *>...

...right lines intersecting each other at right angles, so as to inclose a rectangle. 870. Prob.—Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed...

...right lines intersecting each other at right angles, so as to inclose a rectangle. 870. Prob. — Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed...

...right lines intersecting each other at right angles, so as to inclose a rectangle. 870. Prob. — Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed...