Question

If the equation ax^2+ 4xy + y^2 + ax + 3y + 2 = 0 represents a parabola, then find is the value of a?
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Answer 1

The general form of a parabola is Ax² + Bxy + Cy² + Dx + E y + F = 0

with the parabola restriction that

So in this case A=a ,B=4 and C=1, so by applying EQ1 we have

4² = 4*a*1,

therefore a=4