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FUNDAMENTALS OF MATHEMATICS DIFFERENTIAL CALCULUS by Sanjay Mishra

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TANGENTS INTERSECTING THE CURVE ITSELF

The tangent at P meeting the curve again at Q images

images

FIGURE 4.50

ILLUSTRATION 95: If the tangent at P(1, 1) on y2 = x(2 - x)2 meets the curve again at Q then the point Q is

a. (-1, 2) b. images
c. (4, 4) d. None of these

SOLUTION: (b) Given y2 = x(2 - x)2 Differentiating both sides w.r.t x, 2y y' = (2 - x)2 - 2x(2 - x)

∴ Tangent is y - 1 = -1/2 (x - 1) or 2y = 3 - x

Now, solving 2y = 3 - x with y2 = x (2 - ...

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