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Without writing the equation (y-4)2 = 9(x-4) in the standard form, state whether the graph of this equation is a parabola,circle, ellipse, or hyperbola.

A. parabola

B. ellipse

C. hyperbola

D. circle

Sagot :

sqdancefan

9514 1404 393

Answer:

  A. parabola

Step-by-step explanation:

The curves ellipse, circle, and hyperbola are formed by a relation between the squares of the variables. Here, the y-variable is squared, but the x-variable is not. This equation describes a parabola.

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Additional comments

Its vertex is at (4, 4) and it is compressed horizontally by a factor of 9.

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The hyperbola equation is the difference of squares; the circle and ellipse equations involve the sum of squares. If the variable coefficients are the same, then the sum of squares equation will describe a circle; an ellipse otherwise.

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