Calculus. Graph equation??

Question

Draw the graph of the equation x^4-4x^2-x^2y^2+4y^2=0.
anything will help. thanks

Answer 1

x^2(x^2 - 4) - y^2(x^2 - 4) = 0
x^2(x^2 - 4) = y^2(x^2 - 4)
x^2 = y^2
y = (+ or -)x which would be the lines y = x and y = x.
Plot both of these lines on the same axis and that will be your graph.

Answer 2

If making use of a Graphing Calculator, key in the equation and graph. If no longer, then start up via becoming a table of values. x = -5 ; y = 268 x = -4 ; y = a hundred sixty five x = -3 ; y = 86 x = -2 ; y = 31 x = -one million ; y = 0 { that's an intercept } x = 0 ; y = -7 { that's yet another intercept } x = one million ; y =10 { so we neglected 0 } x = 2 ; y = fifty one x = 3 ; y = 116 Y = 12x^2 + 5x - 7 Y = ( x + one million)( 12x - 7 ) while Y = 0 , then x = -one million or x = 7/12 So the different neglected intercept is at x = 7/12 ; y = 0 The plot will instruct a parabola with a minimum factor. to hit upon this minimum, resolve for the 1st by-product : 0 = 24x + 5 x = -5/24 Then positioned this fee into the unique equation to get the y fee for the minimum factor Y = 12(-5/24)^2 + 5(-5/24) - 7 Y = 25/forty 8 - 25/24 - 7 Y = -361/forty 8

Answer 3

x^4 - 4x^2 - x^2y^2 + 4y^2 = 0
x^2(x^2 - 4) - y^2(x^2 - 4) = 0
(x^2 - y^2)(x^2 - 4) = 0
x^2 - y^2 = 0 or x^2 - 4 = 0
x = y, x = -y, x = 2, x = -2

Four lines.