...given : it will be seen that the three curves are particular cases of what is called a Conic*. A Conic is the locus of a point which moves so that its distance from a fixed point (called the focus) bears a constant ratio to its distance from a fixed straight line called the directrix...

...simplification we get the required equation of the parabola. 26.8 PARABOLA Definition : A parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line. In case of parabola eccentricity is 1 Standard...

...¿. ¿ -¿.* ¿ - ¿ ¿ - ¿ ¿ • -¿1¿ ¿ . ¿ . ¿ . ¿ -a-' -‘¿- - 23. CIRCLES 1. A circle is the locus of a point which moves so that its distance from a fixed point is constant. The fixed point is called the centre of the circle and the constant distance is called...

...curve." Let the latter be a 26 parabola having the equation y— i x. Now a parabola is denned as " the locus of a point which moves, so that its distance from a fixed point is in a constant relation to its distance from a fixed straight line." How do we construct such a curve...

...at B and D meet in O. Prove that L BOD is equal to the difference between L BCD and L BAD. 9. Find the locus of a point which moves so that its distance from a given line is half its distance from a given point on the line. 1O. Prove that, if circles are described...

...whose sines are in a constant ratio. Defined as a locus, the reciprocal curve to a circle is the path of a point which moves so that its distance from a fixed point varies as its distance from a fixed straight line. [Lachlan's Modern Pure Geometry.] II. Solution by...

...In the latter case B will now be at n, if bn = 4 x 10 = 40 miles ; join a, n, and, as before, find the locus of a point which moves so that its distance from b and n is as 17 : 10. This locus will be a circular arc, d^ d^ struck from the centre c2 on the line...

...so that the difference of its distances from (—4, 3) and (4, 3) is numerically equal to 6. 6. Find the locus of a point which moves so that its distance from (4, 0) is twice its distance from the line x=1. 2. SOME IMPORTANT RESULTS Most of the results obtained...

...distance from the point (1, 3) is twice its distance from the line y = - 1 . 21. Determine the equation of the locus of a point which moves so that its distance from the point Q(o, 0) is equal to the distance from the point R(2a, a). 22. Determine the equation of the...

...real points of the curve whose x coordinates are less than unity. EXERCISES 3. 1. Find the equation of the locus of a point which moves so that its distance from the axis of x is twice its distance from the axis of y. 2. A point moves so that twice its distance...