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      "text": "<p>Consider the circle given by the equation \\( (x+4)^2 + (y-4)^2 = 4 \\). What is the location of the center of the circle? What is the circle&#39;s radius?</p>\n",
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        "text": "<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 1: Recall the general form of a circle</strong></div>\r\n\r\n<div class=\"collapsible__body\">\\( (x-h)^2 + (y-k)^2 = r^2 \\) where the center is at \\( (h,k) \\) and the radius is \\( r&nbsp;\\)</div>\r\n</div>\r\n\r\n<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 2: Compare the given equation to the general form</strong></div>\r\n\r\n<div class=\"collapsible__body\">Substituting \\( h = -4\\), \\( k&nbsp;= 4 \\), and \\( r&nbsp;= 2 \\) into the general form reproduces the equation \\( (x+4)^2 + (y-4)^2 = 4 \\)</div>\r\n</div>\r\n\r\n<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 3: Final answer</strong></div>\r\n\r\n<div class=\"collapsible__body\">Center: \\( (-4,4) \\); Radius: \\( r = 2 \\)</div>\r\n</div>\r\n",
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        "text": "<p>\\((\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)</p>\n",
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        "text": "<p>The general form of a circle is \\( (x-h)^2 + (y-k)^2 = r^2 \\), where the center is at \\( (h,k) \\) and the radius is \\( r \\).</p>\r\n",
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        "text": "<p>The general form of a circle is \\( (x-h)^2 + (y-k)^2 = r^2 \\), where the center is at \\( (h,k) \\) and the radius is \\( r \\).</p>\r\n",
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      "text": "<p>What is the center and radius of the circle given by \\( (x+2)^2 + (y-6)^2 = 5 \\)?</p>\n",
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        "text": "<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 1: Recall the general form of a circle</strong></div>\r\n\r\n<div class=\"collapsible__body\">\\( (x-h)^2 + (y-k)^2 = r^2 \\) where the center is at \\( (h,k) \\) and the radius is \\( r \\)</div>\r\n</div>\r\n\r\n<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 2: Compare the given equation to the general form</strong></div>\r\n\r\n<div class=\"collapsible__body\">Substituting \\( h = -2\\), \\( k = 6 \\), and \\( r = \\sqrt{5} \\) into the general form reproduces the equation \\( (x+2)^2 + (y-6)^2 = 5 \\)</div>\r\n</div>\r\n\r\n<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 3: Final answer</strong></div>\r\n\r\n<div class=\"collapsible__body\">Center: \\( (-2, 6) \\); Radius: \\( r = \\sqrt{5} \\)</div>\r\n</div>\r\n",
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      "text": "<p>What is the center and radius of the circle given by \\( (x-2)^2 + (y+9)^2 = 9 \\)?</p>\n",
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        "text": "<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 1: Recall the general form of a circle</strong></div>\r\n\r\n<div class=\"collapsible__body\">\\( (x-h)^2 + (y-k)^2 = r^2 \\) where the center is at \\( (h,k) \\) and the radius is \\( r \\)</div>\r\n</div>\r\n\r\n<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 2: Compare the given equation to the general form</strong></div>\r\n\r\n<div class=\"collapsible__body\">Substituting \\( h = 2\\), \\( k = -9 \\), and \\( r = 3 \\) into the general form reproduces the equation \\( (x-2)^2 + (y+9)^2 = 9 \\)</div>\r\n</div>\r\n\r\n<div class=\"collapsible solution__step\">\r\n<div class=\"collapsible__header\"><strong>Step 3: Final answer</strong></div>\r\n\r\n<div class=\"collapsible__body\">Center: \\( (2, -9) \\); Radius: \\( r = 3 \\)</div>\r\n</div>\r\n",
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        "text": "<p>The general form of a circle is \\( (x-h)^2 + (y-k)^2 = r^2 \\), where the center is at \\( (h,k) \\) and the radius is \\( r \\).</p>\r\n",
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