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Discuss the curve represented by 2x² + 3y² - 8x - 18y + 35 = K. Which statement is correct?
- it is a point if K = 0
- it represents no real locus if K < 0
- it is an ellipse if K > 0
- it is a hyperbola if K > 0
Correct answer: it is a point if K = 0
Solution
Completing the square gives 2(x-2)² + 3(y-3)² = K; this is empty for K<0, a single point for K=0, and an ellipse for K>0.
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