The parametric representation of a point on the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1 / 2 , is

Step-by-step solution

Distance between two foci, 2 a e=7+1=8 a e=4 a=8 ( e= 1 2 given ) Now, array l b²=a² (1-e² )=64 (1- 1 4 ) b²=48 b=4 3 array Since, the centre of the ellipse is the mid point of the line joining two foci, therefore the coordinates of the centre are (3,0) . Its equation is (x-3)² 8² + (y-0)² (4 3 )² =1 Hence, the parametric coordinates of a point on Eq. (i) are (3+8 , 4 3 ) .