...have u = у, z = я /, * = e, and ç y = sin. u ; conjequently и =: :-fc sin. z (sin. z) — t ¡on of a point, the sum of the squares of whose distances from four given pointe in space shall be the least possible. Let one of the pointe be the origin of the...

...respectively. Find the ratio of their areas. 6. Explain what is meant by the locus of a point. Determine the locus of a point, the sum of the squares of whose distances from two given points is constant. What is the limiting case of this problem. 7- The base and hypothenuse of...

...such a way that these planes may '' N 'f intersect in a common line ? 10. Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute "lines" for "planes" in (10). !f\2. Find the equation...

...plane in such a way that these planes may intersect in a common line ? 10. Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute " lines" for "planes" in (10). 12. Find the equation...

...sections of a given sphere made by planes passing through a given point. 367. Locus of a point in space the sum of the squares of whose distances from two fixed points is a given constant.' (Ex. 174.) 368. Locus of a point in space the difference of the squares of whose...

...sections of a given sphere made by planes passing through a given point. 367. Locus of a point in space the sum of the squares of whose distances from two fixed points is a given constant. (Ex. 174.) 368. Locus of a point in space the difference of the squares of whose...

...if 6 = 0, с = 0, the question is satisfied by p = 00, whatever be a, therefore &o. Ex. 5. Find the locus of a point, the sum of the squares of whose distances from a number of given planes is constant. Let tfSipl = (7,, SSj12 = Ct, cfcc. be the equations of the given...

...found in Chauvenet's Elementary (jeumrtry, pp. 230, 236.] 4128. (Proposed by AB EVANS, MA) — Find the locus of a point the sum of the squares of whose distances from the vertices of a given triangle is constant. I. Solution by H. MURPHY. Let the vertices be A, B, C....

...solid angles, faces, and edges of any polyhedron (Euler's theorem) 26 4128. (AB Evans, MA) — Find the locus of a point the sum of the squares of whose distances from the vertices of a given triangle is constant 28 4135. (JJ Walker, MA) — A vertical circle may be...

...their squares is equal to three times the sum of the squares of the sides of the triangle. Ex. 285. The locus of a point, the sum of the squares of whose distances from two fixed points is constant, is the circumference of a circle. Ex. 286. Convert a parallelogram into another having...