Consider the rotated ellipse defined implicitly by the equation 132²-32zy +37y²-45. The quadratic form can be written as 12 VIA[+] - 12 VIPDPT [#] - [ VID["]. where P Hint: What is special about the columns of P? Can you use this to find the matrix D? Once you find D you can plug it into the equation above and perform matrix m a. Using the P defined above, find an equation for the ellipse in terms of u and t. Don't forget to enter the right-hand side too! b. Now drag the points to display the graph of your ellipse on the uv-axes below. to V

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: Write the equation of the parabola given by y? + 2y + 12x – 23 = 0 in standard form. %3D -

A: Given equation of parabola is y2 + 2y + 12x - 23 = 0

Q: Write the general form equation of the parabola that passes through (3,-13) with vertex at (5,-1)

A: We use f(x) =a(x-h)²+k where vertex is (h,k).

Q: Write the equation of a parabola in standard form from the given information Vertex at (2, -2)…

A: Vertex of the parabola is at 2, -2 and focus at 2, -3. Now vertex is, h, k=2, -2⇒h=2  &  k=-2…

Q: Suppose a parabola has vertex (-8, -7) and also passes through the point (-7, -4). Write the…

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Q: Which equation represents the parabola graphed on the coordinate plane below? Ay-x-8²-6 А directrix…

A: Vertex form of parabola with vertex h,k⇒y=ax-h2+k

Q: Find an equation of the parabola with vertex (5,-5) and directrix y=-3   .

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Q: 8) and directrix y = 7? A B y = -(x - 5)² +8 - y=- 1 -(x + 5)² +8 y = -(x + 5)² - 8 D_y==(x + 5)² +8…

A: Given query is to find the equation of the parabola.

Q: A parabola has its vertex at (2,1) and crosses the x-axis at (1,0) and at (3,0). Which of the…

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Q: Write an equation of the parabola in vertex form that passes through (13, 8) and has vertex (3, 2).…

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Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: Find the equation of a sphere if one of its diameters has endpoints: (3, -7, -17) and (17, 7, -3). =…

A: Here we have to find equation of sphere whose one of its diameter has endpoint are given.

Q: Determine the equation of the parabola with vertex (2,8) and x-intercepts 0 and 4 in factored form…

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Q: The standard form of the equation of the parabola with vertex (-2, 5) and point (0, 9) is: = (x +…

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.