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What are the foci of the ellipse of 9 x squared plus 25 y squared plus 100 y - 125 equals 0?
Wiki User
∙ 8y ago
With the equation of an ellipse in the form (x/a)² + (y/b)² = 1 the axes of the ellipse lie on the x and y axes and the foci are √(a² - b²) along the x axis.
9x² + 25y² + 100y - 125 = 0
→ (3x)² + 25(y² + 4y + 4 - 4) = 125
→ (3x)² +25(y + 2)² - 100 = 125
→ (3x)² +25(y + 2)² = 225
→ (3x)²/225 + (y + 2)²/9 = 1
→ (x/5)² + ((y+2)/3)² = 1
Thus the foci are √(5² - 3²) = √16 = 4 either side of the y-axis, but the y axis has been shifted up by 2, thus the two foci are (-4, -2) and (4, -2).
Wiki User
∙ 8y ago
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