Find a new representation of 2x² + 8xy - 1 = 0 by describing it in a system with axes rotated by 30°. Use software (such as Desmos) to include in your submission a graph of the equation, as well as two lines representing the new axes. These line will be in the form y = mx and y = -x Note- the equation in the new system will not necessarily be in the standard form of the hyperbola.

Q: 5. Complete the square to rewrite the following equation in standard form and then identify what…

A: We need to form the standard equation by completing its square. And to check which diagram it…

Q: Find the equation of the parabola by using three points (4,0), (2,8), and (6,0). Step 1. Write the…

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Q: Which equation would shift the parabola down 3 units? A y=z² B y=z² +3 C_y=(z-3)² Dy=(z+3)²³ E =…

A: which equation would shift the parabola down to 3 units.

Q: The line passing through the vertex that divides the parabola into two symmetric parts is . The two…

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Q: 13. Complete the square and find the vertices of this ellipse: 25x² +50x +4y² –16y = 59 A) (-3,2),…

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Q: Write an equation in standard form for a hyperbola with center at (4, 0), vertex (10, 0), and focus…

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Q: Given the equation of a parabola as 12(y-5)=(x+3)^2, determine the following: Direction of…

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Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…