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The ellipse 4x² + 9y² + 12x + 12y + 5 = 0 is confocal with a hyperbola sharing the same principal axes. Which statement is correct?
- the angle between the normals at each point of intersection is 90deg
- the centre of the ellipse is (-3/2, -2/3)
- the distance between the foci of the hyperbola is 2*sqrt(10)/3
- the ellipse and hyperbola have the same length of latus rectum
Correct answer: the centre of the ellipse is (-3/2, -2/3)
Solution
Completing the square gives centre (-3/2, -2/3); confocal ellipse and hyperbola intersect orthogonally, but the verifiable listed fact is the centre.
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