The tangent to the curve y = x 2 - 5 x + 5 , parallel to the line 2 y = 4 x + 1 , also passes through the point :

Step-by-step solution

Equation of line parallel to given line can be taken as y = 2 x + c . Now, this line touches the curve y = x 2 - 5 x + 5 hence, roots of the equation x 2 - 5 x + 5 = 2 x + c ⇒ x 2 - 7 x + 5 - c = 0 must be equal. ⇒ D = 0 ⇒ - 7 2 - 4 · 1 · 5 - c = 0 ⇒ 4 c = - 29 Hence, equation of tangent is 4 y = 8 x - 29 . Clearly, it passes through 1 8 ,   - 7 .