Question
The equation of the ellipse whose one of the vertices is (0, 7) and the corresponding directrix is y = 12, is-
- 95x2 + 144y2 = 4655
- 144x2 + 95y2 = 4655
- 95x2 + 144y2 = 13680
- None of these
Hint:
find out the value of a,b and e from the given values of vertex and directrix equation.
The correct answer is: 144x2 + 95y2 = 4655
144x2 + 95y2 = 4655
Vertex = (0,7) => b=7
Directrix =b/e = 12
=> e= b/12 =7/12
a =b√1-e2
a2 = 49(1- 49/144)= 4655/144
x2/a2+y2/b2= 1
144x2/4655+ y2/49 =1
144x2+ 95y2=4655
this form of ellipse is a vertical one,i.e., the y axis is the major axis and the x axis is the minor axis.
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