What type of conic section is given by the equation 4x^2 + 9y^2 = 36? What are the domain and range
The equation 4x^2 + 9y^2 = 36 represents an ellipse. The constant terms (4 and 9) in front of x^2 and y^2 respectively have different signs, indicating that it is an ellipse rather than a circle.
To find the domain, we solve for x and get:
4x^2 = 36 - 9y^2
x^2 = (36 - 9y^2)/4
x = ±√((36 - 9y^2)/4)
Since the square root of a positive number is always real, x can take any real value. Therefore, the domain of this equation is all real numbers.
To find the range, we solve for y and get:
9y^2 = 36 - 4x^2
y^2 = (36 - 4x^2)/9
y = ±√((36 - 4x^2)/9)
Similarly, since the square root of a positive number is always real, y can also take any real value. Therefore, the range of this equation is all real numbers.