Identify the type of the conic section represented by the equation (9x^2 - 4y^2 = 36).

Question

Accepted Answer

Step:1 ：Step 1: Rewrite the equation in the standard form of conic sections. The standard forms are: [frac{(x-h)^2}{a^2} + frac{(y-k)^2}{b^2} = 1] for ellipse, [frac{(x-h)^2}{a^2} - frac{(y-k)^2}{b^2} = 1] for hyperbola, [(x-h)^2 + (y-k)^2 = r^2] for circle, and [y = ax^2 + bx + c] or [x = ay^2 + by + c] for parabola.Step:2 ：Step 2: Divide the equation by 36 to get [frac{x^2}{4} - frac{y^2}{9} = 1].Step:3 ：Step 3: This equation is in the standard form of a hyperbola where (a^2 = 4) and (b^2 = 9). The terms on the left side of the equation are subtracted, which indicating that the conic section is a hyperbola.

Answer

Step: 1 ：Step 1: Rewrite the equation in the standard form of conic sections. The standard forms are: [frac{(x-h)^2}{a^2} + frac{(y-k)^2}{b^2} = 1] for ellipse, [frac{(x-h)^2}{a^2} - frac{(y-k)^2}{b^2} = 1] for hyperbola, [(x-h)^2 + (y-k)^2 = r^2] for circle, and [y = ax^2 + bx + c] or [x = ay^2 + by + c] for parabola.Step: 2 ：Step 2: Divide the equation by 36 to get [frac{x^2}{4} - frac{y^2}{9} = 1].Step: 3 ：Step 3: This equation is in the standard form of a hyperbola where (a^2 = 4) and (b^2 = 9). The terms on the left side of the equation are subtracted, which indicating that the conic section is a hyperbola.

Identify the type of the conic section represented by the equation $9 x^{2} - 4 y^{2} = 36$ .

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Popular Problems

Identify the type of the conic section represented by the equation 9x2−4y2=36.

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Popular Problems

Identify the type of the conic section represented by the equation $9 x^{2} - 4 y^{2} = 36$ .