question_answer 1)

Find the equation of tangent to the curve y = x2 – 2x + 7 which is (a) Parallel to line 2x – y + 9 = 0 (b) Perpendicular to lien 5y – 15x = 13  

Answer:

(a) Given curve is             y= x2 ? 2x + 7                            ?. (1)       Let P (h, k), be a point on (1)        K = h2 ? 2h + 7                            ?. (2)       Diff. (1) w.r.t. x  = 2x ? 2       M1 = slope of tangent to (1)             M2 = slope of given line 2x ? y + 9 = 0                    According to Question             m1= m2        2h ? 2 = 2  h = 2       (2)  k = (2)2 ? 2(2) + 7 = 7        P(h, k) = (2, 7)       Now equation of tangent to (1) at P is             y ? 7 = m (x ? 2)       2x ? y + 3 = 0. (b)  Given curve is             y = x2 ? 2x + 7               ?..(1)       Let P(h, k) be a point on (1)       k = h2 ? 2h + 7                 ?.. (2)       (1)         m1= slope of tangent to (1)             m2 = slope of given line 5y ? 15y = 13             According to Questions       m1 m2 = 1             (2)              Equation of tangent to (1) is                                36y ? 217 = ?12x + 10        12x + 36 y = 227.