The standard form of the equation of an ellipse is
(x^2 / a^2) + (y^2 / b^2) = 1, where a and b are real numbers so that
a^2 > 0
and
b^2 > 0
We require a^2 and b^2 to be only greater than 0 and not equal to 0 because we can't devide by 0.
So, in order for the given equation to represent an ellipse, we must have
9 - k > 0 and k - 4 > 0
so 9 - k + k > 0 + k and k - 4 + 4 > 0 + 4
or 9 > k and k > 4
That is, 4 < k < 9. So k should be between 4 and 9 both values not inclusive.
-Anonymous