Explanation: The equation of the given curve:
‌

x2

9

+‌

y2

25

=1
On differentiating both sides w.r.t. x , we get
‌

2x

9

+‌

2y

25

‌

dy

dx

‌=1‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
‌

dy

dx

‌=‌

−25x

9y

Since, tangent is parallel to X -axis, then the slope of the tangent is zero.
∴‌‌‌

−25

9

‌

x

y

=0 , which is possible if x=0
Put x=0 in eq (i), we get
‌

y2

25

=1⇒y2=25⇒y=±5
Hence, required points are (0,±5) .