Write the appropriate rotation formulas so that, in a rotated system the equation has no x'y'-term x ^ 2 + 4xy - 2y ^ 2 - 9 = 0 The appropriate rotation formulas are x = and y =

Rewrite the equation in a rotated x′y′​-system without an x′y′​-term. Use the appropriate rotation formulas. For the​ equation, x^2+xy+y^2−19=​0, answer the following question.

#20 parallel to 7x +2y=2 and passes through (3,4). Write standard form

Find the angle of rotation in each problem such that the transformed equation will have no x'y' term.

Give the properties for the equation x 2 - 3y 2 - 8x + 12y + 16 = 0 Center (4, 2) (4, -4) (4, -2)

Standardize the conic whose equation is 7x2 + 4xy + 4y2 - 2x - 6y + 1 = 0.

What will be the new position of the given point (9, - 3) after reflection across the y-axis?

a. At what point should the origin be shifted if the coordinates of a point (4, 5) become (-3, 9)? b.The equation of a curve referred to the new axes, axes retaining their directions, and origin (4, 5) is X^2 + Y^2 = 36. Find the equation referred to the original axes.

What is the image of (4, -7) after a reflection over the y axis?

Standardize the conic with the equation 7x2+4xy+4y2--2x-6y+1=0