Explanation Given: The equation ( x 2 + y 2 − x ) 2 = x 2 + y 2 Calculation: To find the x -intercept let y = 0 in the equation ( x 2 + y 2 − x ) 2 = x 2 + y 2 ( x 2 + 0 2 − x ) 2 = x 2 + ( 0 ) 2 ( x 2 − x ) 2 = x 2 [ x ( x − 1 ) ] 2 = x 2 Taking x common factor inside the bracket x 2 ( x − 1 ) 2 = x 2 ( x − 1 ) 2 = 1 Dividing both sides by x 2 x 2 − 2 x + 1 = 1 Expanding the left hand side x 2 − 2 x + 1 − 1 = 1 − 1 Subtracting 1 from both sides x 2 − 2 x = 0 x ( x − 2 ) = 0 Taking x common on left hand side x = 0 or x − 2 = 0 x = 0 or x = 2 The x -intercept are 0 and 2 To find the y -intercept let x = 0 in the equation ( x 2 + y 2 − x ) 2 = x 2 + y 2 ( 0 2 + y 2 − 0 ) 2 = 0 2 + y 2

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Author: Sullivan

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Chapter 1.2, Problem 85AE

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To find: The intercepts of the graph of the equation ${(x^{2} + y^{2} - x)}^{2} = x^{2} + y^{2}$ and symmetry with respect to $x -axis$ , $y -axis$ and the origin.

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Chapter 1.2, Problem 84AE

Chapter 1.2, Problem 86AE

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The intercepts of the graph of the equation ( x 2 + y 2 − x ) 2 = x 2 + y 2 and symmetry with respect to x -axis , y -axis and the origin.