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Question

# The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x – y + 1 = 0 is

A
x2+y2 – 2xy – 4x – 4y – 4 = 0
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B
x2+y2 – 2xy + 4x – 4y – 4 = 0
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C
x2+y2 + 2xy – 4x + 4y – 4 = 0
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D
x2+y2 + 2xy – 4x – 4y + 4 = 0
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Solution

## The correct option is C x2+y2 + 2xy – 4x + 4y – 4 = 0 Tangent at vertex is x – y + 1 = 0 and focus (0, 0) ∴ Equation of axis of the parabola is x + y = 0 ∴ vertex=(−12, 12) Let equation of directrix be x – y + k = 0 and it passes through (–1, 1) ∴ k = 2 Directrix ≡ x – y + 2 = 0 ∴ Equation of parabola (x−y+2√2)2=x2+y2⇒x2+y2+2xy−4x+4y−4=0

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