SOLUTION: Please help me with this! Find the centre, vertices, lenght of latus rectum, foci , eccentricities of the ellipse x^2 + 9y^2 + 4x -18y - 23 = 0
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Question 991825: Please help me with this! Find the centre, vertices, lenght of latus rectum, foci , eccentricities of the ellipse x^2 + 9y^2 + 4x -18y - 23 = 0
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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x^2 + 9y^2 + 4x -18y - 23 = 0
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Complete the squares:
= = .
So, you have the equation
+ = ,
or, in the canonical form,
+ = .
It is a canonical equation of an ellipse.
Its center is at the point (x,y) = (-2,1). Semi-major and semi-minor axes are 6 and 2, respectively: a=6 and b=2.
Semi-major axis is the distance from the ellipse' center to its vertices.
Linear eccentricity is = = . It is the distance from the ellipse's center to its foci.
Next, take the textbook and determine the rest ellipse's characteristics you need.
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