The equation represents
An ellipse
Identifying the curve:
Given
The standard form of the equation is
Comparing the above equation with the given equation, we get
We know that the condition for straight lines is given by
Substituting the values, we get
Discriminant
We know that if , then the curve represents either a circle or an ellipse.
Now from the values, we know .
For a curve to be an ellipse, and . This proves that the given curve is an ellipse.
Hence, option (C) is the correct answer.