Recognising the equation of a circle.
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\nIf an equation is written in the form $cx^2+dx+ey^2+fy+g=0$, where $c,d,e,f,g$ are numbers, it could be a circle, but it might be something else (for example, an ellipse, a hyperbola, or even an empty graph). If the coefficients of $x^2$ and $y^2$ are the same then the equation is of a circle. These values being the same allow us to divide by that coefficient and start completing the square to get the equation in to the standard form of a circle.
", "tags": ["circles", "graphing"], "parts": [{"distractors": ["", "", "This is the equation of two vertical parallel lines", "This is the equation of an ellipse", "", "This is the equation of an ellipse", "This is the equation of a hyperbola"], "matrix": ["1", "1", 0, 0, "1", 0, 0], "displayColumns": 0, "warningType": "none", "type": "m_n_2", "displayType": "checkbox", "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "minAnswers": 0, "choices": ["$\\simplify[all]{(x-{ccx})^2+(y-{ccy})^2={rs[0]}}$
", "$\\simplify[all]{x^2+(y-{ccy})^2={rs[1]}}$
", "$\\simplify[all]{(x-{ccx})^2={rs[2]}}$
", "$\\simplify[all]{{xmult}(x-{ccx})^2+{ymult}(y-{ccy})^2={rs[3]}}$
", "$\\simplify[all]{{ax}x^2+{bx}x+{ax}y^2+{by}y={rs[4]}}$
", "$\\simplify[all]{{ax}x^2+{bx}x+{ay}y^2+{by}y={rs[5]}}$
", "$\\simplify[all]{x^2+{bx}x-y^2+{by}y={rs[5]}}$
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