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Show that the line 2x – y + 2 = 0 is a tangent to the parabola y2 = 16x. Find the point of contact also. |
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Answer» Given line is 2x – y + 2 = 0 ⇒ y = 2x + 2 Comparing with y = mx + c we get m = 2, c = 2 Comparing y2 = 16x with y2 = 4ax We get 4a = 16 ⇒ a = 4 a/m = 4/2 = 2 = c ∴ Point of contact = (a/m2, 2a/m) = (4/22, 2(4)/2) = (1, 4) |
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