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The tangent at (1,7) to the curve x^(2) = y - 6x touches the circle x^(2) + y^(2) + 16x + 12 y + c = 0 at |
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Answer» (6,7) `x (1) = (1)/(2) (y + 7) - 6` [replacing `x^(2) to xx_(1)` and `2y to y + y_(1)`] `implies 2x = y + 7 - 12` `implies y = 2x + 5` Which is also tangents to the circle `x^(2) + y^(2) + 16X + 12 y + c = 0` i.e., `x^(2) + (2x + 5)^(2) + 16x + 12 (2x + 5) + C = 0` must have equal, ROOLS i.e., `alpha = beta` `implies 5x^(2) + 60x + 85 + c = 0` `implies alpha + beta = (-60)/(5)` `implies alpha = - 6` `:. x = - 6` and `y = 2x + 5 = - 7` `:.` POINT of contact is (-6, -7). |
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