x^2+y^2=25

{ "query": { "display": "$$x^{2}+y^{2}=25$$", "symbolab_question": "CONIC#x^{2}+y^{2}=25" }, "solution": { "level": "PERFORMED", "subject": "Geometry", "topic": "Circle", "subTopic": "formula", "default": "(a,b)=(0,0),r=5" }, "steps": { "type": "interim", "title": "$$x^{2}+y^{2}=25:\\quad$$Circle with center at $$\\left(0,\\:0\\right)\\:$$and radius $$r=5$$", "input": "x^{2}+y^{2}=25", "steps": [ { "type": "definition", "title": "Circle Equation", "text": "$$\\left(x−a\\right)^2+\\left(y−b\\right)^2=r^2\\:\\:$$is the circle equation with a radius r, centered at $$\\left(a,\\:b\\right)$$" }, { "type": "step", "primary": "Rewrite $$x^{2}+y^{2}=25\\:$$in the form of the standard circle equation", "result": "\\left(x-0\\right)^{2}+\\left(y-0\\right)^{2}=5^{2}" }, { "type": "step", "primary": "Therefore the circle properties are:", "result": "\\left(a,\\:b\\right)=\\left(0,\\:0\\right),\\:r=5" } ], "meta": { "solvingClass": "Circle" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "funcsToDraw": { "funcs": [ { "evalFormula": "y=\\sqrt{5^{2}-x^{2}}", "displayFormula": "x^{2}+y^{2}=5^{2}", "attributes": { "color": "PURPLE", "lineType": "NORMAL", "isAsymptote": false } }, { "evalFormula": "y=-\\sqrt{5^{2}-x^{2}}", "displayFormula": "x^{2}+y^{2}=5^{2}", "attributes": { "color": "PURPLE", "lineType": "NORMAL", "isAsymptote": false } } ] }, "pointsToDraw": { "pointsLatex": [ "(0,0)" ], "pointsDecimal": [ { "fst": 0, "snd": 0 } ], "attributes": [ { "color": "PURPLE", "labels": [ "\\mathrm{Center}" ], "labelTypes": [ "DEFAULT" ], "labelColors": [ "PURPLE" ] } ] }, "linesToDraw": [ { "p1x": "0", "p1y": "0", "p2x": "3.5355339059327", "p2y": "3.5355339059327", "attributes": { "color": "GRAY", "lineType": "BOLD", "labels": [ "\\mathrm{radius=}5" ], "isAsymptote": false } } ], "functionChanges": [ { "origFormulaLatex": [], "finalFormulaLatex": [], "plotTitle": "x^{2}+y^{2}=5^{2}", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -11.25, "xMax": 11.25, "yMin": -11.25, "yMax": 11.25 } }, "showViewLarger": true } } }