The equation x^2 2- + y^2 -5 +1=0 represents an ellipse, if

Step-by-step solution

The given equation is x^2 2- + y^2 -5 + 1 = 0 . Rearranging the equation, we get x^2 -2 + y^2 5- = 1 . For this equation to represent an ellipse, the denominators must be positive and distinct. Thus, we require -2 > 0 and 5- > 0 . From -2 > 0 , we have > 2 . From 5- > 0 , we have Combining these inequalities, we get 2 Additionally, for the equation to represent an ellipse, the denominators must not be equal, i.e., -2 5- , which implies 2 7 or 3.5 . Since 3.5 is within the interval (2, 5) , the condition 2 Answer: 2