Identify the graph of x^2-8y=0 for theta=90º and write and equation of the translated or rotated graph in general form.

Answer:The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)Step-by-step explanation:* At first lets talk about the general form of the conic equation- Ax² + Bxy + Cy²  + Dx + Ey + F = 0∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse. ∵ B² - 4AC = 0 , if a conic exists, it will be a parabola. ∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.* Now we will study our equation:* x² - 8y = 0∵ A = 1 , B = 0 , C = ∴ B² - 4AC = (0)² - 4(1)(0) = 0 ∵ B² - 4AC = 0 ∴ it will be a parabola.∵ Ф = 90°* The point (x , Y) will be (x' , y')∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ∵ cos(90) = 0 and sin(90) = 1∴ x = -y' and y = x'* lets substitute x and y in the first equation∴ (-y')² - 8(x') = 0∴ (y')² - 8x' = 0* We notice that the x' took the place of y and y' took the place of x∴ The parabola rotated around the origin by 90°∴ The equation of the parabola is (y')² - 8x' = 0* The answer is parabola, with angle of rotation 90°* The equation is (y')² - 8x' = 0* Look to the graph- The blue is x² - 8y = 0- The green is (y')² - 8x' = 0