...investigating the equation to the ellipse which is sometimes employed as follows. 118. To find the locus of a point, the sum of whose distances from two given points is constant. Through the two fixed points S, H (fig. 40), draw the indefinite line Sx; bisect SH in C, and draw...

...required coordinates are a;'=5^, y'=~fs Ex. (4). Investigate the equation to the curve that is the locus of a point, the sum of whose distances from...constant. Let S, H be the two fixed points, and take C the middle point of SH as origin. Let P be a point on the locus, and let SP+HP=2a, and SH=2c. ^ MH...

...SB-BP; but AP=BP; .'. HP + SP=HA + SB, the sum of the given radii, and therefore constant. And the locus of a point, the sum of whose distances from two given points is constant, is an ellipse. (See the 4th of the worked Examples.) 12. If a;', y' were the coordinates of the point...

...(external or internal) whose product is equal to a given constant, fc*. (III. 56, 59.) 172. Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant It. 173. Find the locus of a point the difference of whose...

...(external or internal) whose product is equal to a given constant, k'. (III. 56, 59.) 172. Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant k. 173. Find the locus of a point the difference of whose...

...Find the locus of the. foot of the perpendicular from the focus on the tangent. 14. Prove that the locus of a point the sum of whose distances from two given points is constant is such that the distance of any point in it from a fixed straight line bears a constant ratio to its...

...Find the locus of the foot of the perpendicular from the focus on the taugeiit. 14. Prove that the locus of a point the sum of whose distances from two given points is constant is such that tho distance of any point in it from a fixed straight Hue bears a constant ratio to its...

...given circle into segments whose product is equal to a given constant, /<? (33, Exercise). 21, Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k. (v. I., Exercise 10.) 22, Find the locus of a point...

...given straight lines are in a given ratio. (The locus consists of two straight lines.) 462. Find the locus of a point the sum of whose distances from two given straight lines is equal to a given length k. (See Ex.- 73.) PROBLEMS. 463. Given the perimeters of...

...circle into segments who.-*- product is equal to a given constaut, k* (33, Exercise). 91. Find the locus of a point the sum of whose distances from two given straight Hues is equal to a given constant, k. (v. I., Exercise 10.) 28. Find the locus of a point...