At-what-point-of-the-parabola-y-x-2-will-the-tangent-a-be-parallel-to-the-line-y-4x-5-b-be-perpendicular-to-2x-6y-5-0-c-make-an-angle-of-45-with-3x-y-1-0-

Question Number 93855 by Ar Brandon last updated on 15/May/20

At what point of the parabola y = x^{2}

will the tangent

a ∖ be parallel to the line y = 4 x - 5

b ∖ be perpendicular to 2 x - 6 y + 5 = 0

c ∖ make an angle of 45^{°} with 3 x - y + 1 = 0

Answered by Kunal12588 last updated on 15/May/20

a ⟩ w h e n 2 x = 4 \Rightarrow x = 2; p o i n t (2, 4)

b ⟩ w h e n \frac{- 1}{2 x} = \frac{1}{3} \Rightarrow x = \frac{- 3}{2}; p o i n t (- \frac{3}{2}, \frac{9}{4})

c ⟩ w h e n 1 = \frac{2 x - 3}{1 + 6 x} \Rightarrow 4 x = - 4 \Rightarrow x = - 1; p o i n t (- 1, 1)