 | George Russell Briggs - 1887 - 170 pages
...lines Ax + By + C = o and A1 x + B' y + C1 — o are Ax + JSy+C = ± A'x + B'y+C1 ~ ~ (L/) A point moves so that the sum of the squares of its distances from the four sides of a given square is constant ; show that the locus of the point is a circle ; find... | |
 | John Bascombe Lock - Forces and couples - 1888 - 278 pages
...position, magnitude and direction by the three sides of a given triangle not taken the same way round ; find the locus of a point which moves so that the sum of the moments of the three forces about it may be constant. 6. Prove that the moment of a given force about... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...the sum of the squares on its diagonals the quadrilateral is a parallelogram. Ex. 511. — A point moves so that the sum of the squares of its distances from four given points is constant Show that its locus is a circle. Ex. 512. — The sum of the squares of the distances of a point from... | |
 | 1890 - 608 pages
...1. Find the length of the perpendicular from the point hh upon the straight line Ax + By + C — 0. Find the locus of a point which moves so that the sum of the perpendiculars from it upon two given straight lines is constant. 2. Two tangents can be drawn from... | |
 | De Volson Wood - Geometry, Analytic - 1890 - 372 pages
...intersection of AP and BQ is a circle whose centre is in the given circle, and radius is V%R. 35. A point moves so that the sum of the squares of its distances from the four sides of a square is constant; show that the locus of the point is a circle. 36. Show that... | |
 | Euclid - Geometry - 1892 - 460 pages
...4. Find the locus of a point at a given radial distance from the circumference of a given circle. 5. Find the locus of a point which moves so that the sum of its distances from two given intersecting straight lines of unlimited length is constant. 6. Find the... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...focus and directrix. 706. Given two points and the focus, to find the directrix. THE ELLIPSE. 838. The locus of a point which moves so that the sum of its distances from two fixed points is constant is called an ellipse. The fixed points are called the... | |
 | W. J. Johnston - Geometry, Analytic - 1893 - 448 pages
...19. If APB = a constant /3 ; find the locus of P. Ans. The circle x2 + y2 — 2 ay cot ß = a2. 20. Find the locus of a point which moves so that the sum of the squares of its distances from the sides of a square (side = a) is constant = 2 k2. Ans. Taking two adjacent sides of square as axes,... | |
 | W. J. Johnston - Geometry, Analytic - 1893 - 462 pages
...the mean centre of the given points. 10. If rni PA2 + ТЦ PB2 + m3 PC2 + &c- = constant, 11. A point moves so that the sum of the squares of its distances from the sides of a regular polygon is constant : show that its locus is a circle. [Equation to locus is... | |
 | George Albert Wentworth - 1894 - 362 pages
...2MP=2y. Substituting these values in (1), we have or 3y2 = x2, as the required equation. 20. A point moves so that the sum of the squares of its distances from the two fixed points (a, 0) and (— a, 0) is the constant 2£2; find the equation of its locus. Let... | |
| |
Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from... 
