...b This equation is satisfied by the co-ordinates of F. That is, F lies on the line aft. (3) A point moves so that the difference of the squares of its distances from two given points is constant. Find the locus of the point. Take the line joining the two given points A,...

...b This equation is satisfied by the co-ordinates of F. That is, F lies on the line a/3. (3) A point moves so that the difference of the squares of its distances from two given points is constant. Find the locus of the point. Take the line joining the two given points A,...

...projection of the medial line of this last side on its direction. The geometrical locus of the point, such that the difference of the squares of its distances from two fixed points is constant, is a straight line perpendicular to that which joins the fixed points. 110. Draw through...

...a, 0) is constant (2c2) ; find the equation of its locus. Ans. x2 + ?/2 = c2 - a2. JEx. 3. A point moves so that the difference of the squares of its distances from the two fixed points (a, 0) and ( - a, 0) is constant (c!) ; find the equation of its locus. Ans. iax...

...fixed points (a, 0) and ( — a, 0) is the constant 2/fc2; find the equation of its locus. 21. A point moves so that the difference of the squares of its distances from (a, 0) and ( — a, 0) is the constant A:2 ; find the equation of its locus. Exercise 10. (Review.)...

...inclination of tho tangent is that of tho conjugate diameter. The Hyperbola. DEF. — A hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points (the foci) is constant. The hyperbola may be treated in the same...

...conjugate diameters is equal to the rectangle contained by the axes of the ellipse. THE HYPERBOLA. 883. The locus of a point which moves so that the difference of its distances from two fixed points is constant is called an hyperbola. The fixed points are called...

...Obtain Oa)2 + y2 + (x + a)2+y2 = 2^ or x2 + y2 = № — a?, as the required equation. 21. A point moves so that the difference of the squares of its distances from (a, 0) and (— a, 0) is the constant £2; find the equation of its locus. Let (x, г/) be the moving...

...the squares of the distances from two given points is fixed. The same for three given points. 145. Find the locus of a point which moves so that the...squares of its distances from two fixed points is constant. 146. Within a circle two chords at right angles to each other intersect in a fixed point....

...the distance apart of the luminous points and by the ratio TO -i- n. V 173 137. Given two circles. Find the locus of a point which moves so that the difference of the squares on the tangents from it to the two circles shall be constant. NOTE. — When the difference is 0, the...