Q. 195.0( 4 Votes )

Find the equation

Answer :

To find the equation of the tangent to the curve, we first need to find the slope of the tangent to the curve.

Slope of the tangent to the curve y is given by .


We have,






Dividing numerator and denominator by (x – 2)(x – 3),




And we have, . So, replace the value by y in the above equation.



We know that the tangent cuts the x-axis. This means that,


y = 0


Take



(x – 2)(x – 3) × 0 = x – 7


x – 7 = 0


x = 7


We have thus got the point which cuts the x-axis, that is, (7, 0).


We need to find the slope of the tangent at point (7, 0). So,






Now, equation of the tangent at point (x, y) with slope m is given by,


y – y1 = m(x – x1)


Now, replace x1 by 7, y1 by 0 and m by 1/20.



20y = x – 7


x – 20y – 7 = 0


Thus, equation of the tangent to the curve is x – 20y – 7 = 0.


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