The general form of the equation of an ellipse is 4x2+9y2−64x+72y+364=0. Write the equation in standard form and give the coordinates of the center, the length of the major axis, and the length of the minor axis. Then graph the ellipse.
Also one more question on hyperbolas if you don't mine :/
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The general form of the equation of a hyperbola is 16x2−y2+32x+2y−1=0. Write the equation of this hyperbola in standard form and give the coordinates of the center, the coordinates of the vertices, and the equations of the asymptotes. Thengraph the hyperbola.
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Thank you so much guys.
+130466 4x^2 + 9y^2 -64x + 72y + 364 = 0 Subtract 364 from both sides
4x^2 + 9y^2 -64x + 72y = -364 Complete the square on x and y
4(x^2 - 16x + 64) +9(y^2 + 8y + 16) = -364 + 256 + 144
4(x - 8)^2 + 9(y + 4)^2 = 36 divide both sides by 36
(x-8)^2 / 9 + (y+4)^2 / 4 = 1
The center is (8, -4)
The length of the major axis = 2(3) = 6
The length of the minor axis = 2(2) = 4
+130466 Hyperbola
16x^2 - y^2 +32x +2y - 1 = 0 Add 1 to both sides
16x^2 - y^2 +32x +2y = 1 Complete the square on x and y
16(x^2 + 2x + 1) - (y^2 - 2y +1) = 1 + 16 -1
16(x + 1)^2 - (y -1)^2 = 16 divide both sides by 16
(x+1)^2 - (y-1)^2 / 16 = 1
The center is (-1, 1)
The vertices are (-1± a, 1) = (-2,1) and (0,1)
The equations of the asymptotes are y =±b/a = ±4x
