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Find the equation of the parabola if its focus is at the origin and the tangent at its vertex is given by x - y + 1 = 0.
- x² + y² + 2xy - 4x + 4y - 4 = 0
- x² - 4x + 4y - 4 = 0
- y² - 4x + 4y - 4 = 0
- 2x² + 2y² - 4xy - x + y - 4 = 0
Correct answer: x² + y² + 2xy - 4x + 4y - 4 = 0
Solution
The correct option represents a parabola with its focus at the origin and aligns with the given tangent line at the vertex, confirming that it satisfies the conditions of the problem.
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