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Consider the two curves `C_1` ; `y^2 = 4x`, `C_2` : `x^2 + y^2 - 6x + 1 = 0` then :A. `C_(1)" and "C_(2)` touch each other at one pointB. `C_(1)" and "C_(2)` touch eacth other exactly at two pointC. `C_(1)" and "C_(2)` intersect ( but do not touch) at exactly two pointsD. `C_(1)" and "C_(2)` neither intersect not touch each other |
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Answer» Correct Answer - B The x-coordinates of the points of intersection of `C_(1)" and "C_(2)` are roots of the equation `x^(2)+4x-6x+2=0rArrx=1` Putting x = 1 in `y^(2)=4x`, we get `y = +- 2`. Thus, two curves intersect at (1, 2) and (1, -2). Equations of tangents to `C_(1)" and "C_(2)` at (1, 2) are `2y=2(x+1)" and "x+2y-3(x+1)+1=0` `"or, y=x+1 and y=x+1"` Thus, `C_(1)" and "C_(2)` touch each other at P(1, 2). Similarly, `C_(1)" and C_(2)` have the same tangent x + y + 1 = 0 at Q(1, -2). |
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