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The condition for the two curves to touch each other is that they should both have a common tangent at a particular (x,y) :Hence, say they meet at (x1,y1). The slope of tangent at this point for both curves should be equal.dy/dx = 8x1 + 2dy/dx = 3(x1)^2 - 1Hence, 3(x1)^2 - 1 = 8x1 + 2Therefore, 3(x1)^2 - 8x1 - 3 =0x1 = 3, -1/3Now put x1 in both curves and find the value of y1. Only the value of y1 is same for both curves for x1 = 3 which is y1 = 34Hence, they meet each other at (3, 34).Thanks & RegardsBharat BajajaskIITians FacultyQualification.IIT Delhi
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