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Find Equation of an Ellipse?
Find the Equations of the Ellipses Satisfying the given conditions. The center of each is at the origin.
Vertex (8, 0)
Pass through (2, 3)
The only part I seem to be getting correct so far is the squaring of 8 to 64, as the final answer should be:
X^2/64 + 15y2/144 = 1
or
3x^2 + 20y^2 = 192
1 Answer
- ?Lv 78 years agoFavorite Answer
The circle composed using the major axis is x² + y² = 8² which is x²/8² + y²/8² = 1
The point (2, y>0) on this circle is at (2,√(64-4)) = (2,√60) = (2,2√15)
But the point on the ellipse is (2,3), so the y axis is compressed by 2√15 / 3 so
(x/8)² + (y*√15 / 12)² = 1 which is
x²/64 + 15y²/144 = 1
Q.e.D.