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Find the diameter of the circle defined by an equation x2 + y2 - 4x + 4y - 28 = 01. 122. 103. 84. 6 |
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Answer» Correct Answer - Option 1 : 12 Concept: The general equation of a second-degree curve is \(\rm ax^2+2hxy+by^2+2gx+2fy+c =0\) Where a, b, c, f, g, h are constant If a = b ≠ 0 and h = 0, then it represents a circle. The general equation for the circle \(\rm ax^2+ay^2+2gx+2fy+c =0\) The radius of that circle = \(\rm \sqrt{\left({g\over a}\right)^2+\left({f\over a}\right)^2-\left({c\over a}\right)}\)and center \(\rm \left(-{g\over a},-{f\over a}\right)\) Area of a circle = πr2 Calculation: Given equation of the circle is: ⇒ x2 + y2 - 4x + 4y - 28 = 0 Comparing to the general equation of a circle \(\rm ax^2+ay^2+2gx+2fy+c =0\) a = 1, g = -2, f = 2, c = -28 Radius = \(\rm \sqrt{\left({g\over a}\right)^2+\left({f\over a}\right)^2-\left({c\over a}\right)}\) ⇒ R = \(\rm \sqrt{\left({-2}\right)^2+\left({2}\right)^2-\left({-28}\right)}\) ⇒ R = \(\rm \sqrt{4+4+28}\) ⇒ R = \(\rm \sqrt{36}\) = 6 Diameter = 2R D = 2 × 6 = 12 |
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