Identify the graph of the given nondegenerate conic sections: y^2 - 12x - 4y + 52 = 0

Question
Conic sections
asked 2021-02-21
Identify the graph of the given nondegenerate conic sections: \(y^2 - 12x - 4y + 52 = 0\)

Answers (1)

2021-02-22
Step 1 A nondegenerate conic section of the form \(Ax^2 + Cy^2 + Dx + Ey + F = 0\) a)If \(A = C\) then circle b)If \(AC = 0\) then the parabola c)If \(A \neq C\) and \(AC > 0\) then the ellipse d)If \(AC < 0\) then hyperbola. Step 2 Given equation of conics is \(y^2 - 12x - 4y + 52 = 0\) comparing with \(Ax^2 + Cy^2 + Dx + Ey + F = 0\) gives \(A=0 ,C=1 , D=-12 , E=-4 , F=0\) Here \(AC = 0 (1) = 0\) Therefore the graph of the given equation is parabola.
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