Question

Find the equation for the ellipse that satisfies the given conditions:

(i) Ends of major axis (±3, 0) ends of minor axis (0, ±2) 

(ii) Ends of major axis (0, ±√5), ends of minor axis (±1, 0) 

(iii) Length of major axis 26, foci (±5, 0) 

(iv) Length of major axis is 20, foci (0, ±5) 

(v) Length of minor axis is 16, foci (0, ±6) 

Answer 1

(i) Given: Ends of major axis (±3, 0) ends of minor axis (0, ±2) 

i.e., (± a, 0) = (±3, 0) and (0, ±b) = (0, ±2)

∴ a = 3 and b = 2 

Required equation of the ellipse is

x²/a² + y²/b² = 1 i.e., x²/9 + y²/4 = 1

(ii) Given: Ends of major axis  (0, ± √5), ends of minor axis (±1, 0) 

Since ends of major axis lie on the y-axis, then required equation of the ellipse is,

(iii) Given: Length of major axis 26, foci (±5, 0) 

Since, foci lie on the x-axis, t hen required equation of the

x²/a² + y²/b² = 1

We have, length of major axis = 2a = 26 (given) and foci = (±c, 0) = (±5, 0)

(iv) Given: Length of minor axis is 16, foci (0, ±6) 

Since, foci lie on the y-axis, then required equation of the ellipse is

(v) Given: Length of minor axis is 16, foci (0, ±6) 

Since, foci lie on the y-axis, then required equation of the ellipse is