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Which type of conic section does the following equation represent?left bracket, x, minus, 7, right bracket, squared, equals, minus, 28, left bracket, y, plus, 6, right bracket(x−7) 2 =−28(y+6)

Question

Which type of conic section does the following equation represent?left bracket, x, minus, 7, right bracket, squared, equals, minus, 28, left bracket, y, plus, 6, right bracket(x−7) 2 =−28(y+6)

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Solution

The given equation is in the form of (x-h)² = -4a(y-k), which represents a downward-opening parabola. Here, h = 7, k = -6, and a = -7. The negative sign indicates that the parabola opens downwards.

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