question_answer 53)

Find the equation of normal to the curve y = x3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0. 

Answer:

Given curve :             y = x3 + 2x +  6             ?.. (1)       Let P (h, k) be a point on (1)                         ?. (2)       (1)       m1 = slope of tangent to (1)                   slope of normal to (1)       According to question, slope of normal = slope of given line             x + 14 y + 4 = 0                                     When h = 2, then       K = 8 + 4 + 6 = 18       When h = ?2 then             K = ?8 ? 4 + 6 = ?6 [By (2)]        P(h, k) = (2, 18) and (?2, ?6)       equation of normal to (1).       At (2, 18) is                   and At (?2, ?6) is