Question
Identify the conic 16x^2+y^2=81 explain how
Answers
GPT 3.5
The given equation, 16x^2 + y^2 = 81, represents an ellipse.
To demonstrate this, we can rewrite the equation in standard form for an ellipse:
(x^2)/(a^2) + (y^2)/(b^2) = 1
First, we need to divide the given equation by 81 to make the right side of the equation equal to 1:
(16x^2)/(81) + (y^2)/(81) = 1
Next, we find a and b by taking the square root of the denominators of the x^2 and y^2 terms, respectively:
a = sqrt(81/16)
a = 9/4
b = sqrt(81)
b = 9
Therefore, the standard form will be:
(x^2)/((9/4)^2) + (y^2)/9^2 = 1
(x^2)/(81/16) + (y^2)/81 = 1
16x^2 + 81y^2 = 81
Thus, the given equation 16x^2 + y^2 = 81 represents an ellipse.
To demonstrate this, we can rewrite the equation in standard form for an ellipse:
(x^2)/(a^2) + (y^2)/(b^2) = 1
First, we need to divide the given equation by 81 to make the right side of the equation equal to 1:
(16x^2)/(81) + (y^2)/(81) = 1
Next, we find a and b by taking the square root of the denominators of the x^2 and y^2 terms, respectively:
a = sqrt(81/16)
a = 9/4
b = sqrt(81)
b = 9
Therefore, the standard form will be:
(x^2)/((9/4)^2) + (y^2)/9^2 = 1
(x^2)/(81/16) + (y^2)/81 = 1
16x^2 + 81y^2 = 81
Thus, the given equation 16x^2 + y^2 = 81 represents an ellipse.