AP EAMCET Engineering 18 Sep 2020 Shift 1 Paper

The standard form of the equation for an ellipse centered at the origin is:
‌

x2

a2

+‌

y2

b2

=1
where a and b are the lengths of the semi-major and semi-minor axes, respectively. The vertices of the ellipse are located at (±a,0) and (0,±b).
In this problem, we are given the vertices (5,0) and (0,−4), which correspond to the points (a,0) and (0,−b), respectively. So we have:
a=5 and b=4
Substituting these values into the standard form of the equation for an ellipse, we get:
‌

x2

52

+‌

y2

42

=1
Simplifying and rearranging, we get:
‌

x2

25

+‌

y2

16

=1
So the equation of the ellipse is boxed‌‌

x2

25

+‌

y2

16

=1.