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Ava-May Nelson

Answered question

2021-02-21

Identify the graph of the given nondegenerate conic sections:

y^{2} - 12 x - 4 y + 52 = 0

Malena

Skilled2021-02-22Added 83 answers

Step 1 A nondegenerate conic section of the form

A x^{2} + C y^{2} + D x + E y + F = 0

a)If

A = C

then circle b)If

A C = 0

then the parabola c)If

A \neq C

and

A C > 0

then the ellipse d)If

A C < 0

then hyperbola. Step 2 Given equation of conics is

y^{2} - 12 x - 4 y + 52 = 0

comparing with

A x^{2} + C y^{2} + D x + E y + F = 0

gives

A = 0, C = 1, D = - 12, E = - 4, F = 0

Here

A C = 0 (1) = 0

Therefore the graph of the given equation is parabola.

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