question_answer 1)

At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (–4, –3). Find the equation of the curve, given that it passes through (–2, 1) 

Answer:

We know that the slope of the line segment joining the points (x, y) and (?4, ?3) is .       Also the slope of the tangent to the curve       It is given that             Integrating both sides, we have                         As it passes through point (?2, 1)       log(1 + 3) = log (?2 + 4)2 + C                                     which is the required curve.