MATH SOLVE

3 months ago

Q:
# Write and equation of the translated or rotated graph in general form (picture below)

Accepted Solution

A:

Answer:The answer is ellipse; 3x² + y² + 6x - 6y + 3 = 0Step-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:* 3x² + y² = 9∵ A = 3 , B = 0 , C = 1∴ B² - 4 AC = (0)² - 4(3)(1) = -12∴ B² - 4AC < 0∴ The graph is ellipse or circle* If A and C are nonzero, have the same sign, and are not equal to each other, then the graph is an ellipse.* If A and C are equal and nonzero and have the same sign, then the graph is a circle.∵ A and C have same signs with different values∴ It is an ellipse* Now lets study T(-1 , 3), that means the graph will translate 1 unit to the left and 3 units up∴ x will be (x - -1) = (x + 1) and y will be (y - 3)* Lets substitute the x by ( x + 1) and y by (y - 3) in the equation∴ 3(x + 1)² + (y - 3)² = 9 * Use the foil method∴ 3(x² + 2x + 1) + (y² - 6y + 9) = 9* Open the brackets∴ 3x² + 6x + 3 + y² - 6y + 9 = 9* Collect the like terms∴ 3x² + y² + 6x - 6y + 12 = 9∴ 3x² + y² + 6x - 6y + 12 - 9 = 0∴ 3x² + y² + 6x - 6y + 3 = 0* The answer is ellipse of equation 3x² + y² + 6x - 6y + 3 = 0