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The equation of the common tangents to the parabola y = x2 and y = –(x – 2)2 is / are (a) y = 4(x–1)(b) y = 0 (c) y = –4(x–1) (d) y = –30x–50 |
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Answer» Correct option (a),(b) Explanation: Let y = mx + c is tangent to y = x2 mx + c = x2 ⇒ x2– mx – c = 0 has equal roots m2 + 4c = 0 y = mx – m2/4 is tangent to y = –(x–2)2 also mx – 4 m2 = –x2 + 4x – 4 x2 +(m – 4)x + 4 - m2/4 = has equal roots (m – 4)2 - 4(4 - m2/4) = 0 m2 + 16 – 8m – 16 + m2 = 0 m2 – 4m = 0 m = 0, 4 Equation of tangent are y = 0 and y = 4x – 4 |
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