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We have y^2 = 20x . Let (x1,y1) be the tangential point Now 2yy′ = 20 ∴ y′ = 10/y ie., at (x1, y1) m = 10/y1 …(1) But the tangent makes an angle 45° with the x – axis. ∴ slope of the tangent m=tan 45° = 1 … (2) From (1) and (2) 10/y1 = 1 ⇒ y1 = 10 But (x1,y1) lies on y^2 = 20x ⇒ y1^2 = 20 x1 100 = 20(x1) or x1 = 5 i.e., (x1,y1) = (5,10) and hence the equation of the tangent at (5, 10) is y – 10 = 1(x – 5) y = x + 5