How do you identity if the equation #y+4=(x-2)^2# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

1 Answer

Answer:

The given equation is a Parabola

Explanation:

Given -

#(y+4)=(x-2)^2#

Let us rewrite the equation in a know form

#y+4=x^2-4x+4#
#ycancel (+4)-x^2-4xcancel(-4)=0#

#-x^2-4x+y=0#

Let us have the coics section equation

#Ax^2+Cy^2+Dx+Ey+F=0#

If the product of the coefficient of #x^2# and #y^2# is equal to zero, then the given equation is a Parabola.

In the given equation there is no #y^2# term. The coefficient of #y^2# is zero. Hence the product of the coefficients of #x^2# and #y^2# is equal to zero.

The given equation is a Parabola.

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