Determine the coordinates of the vertex and the axis of symmetry of the parabola defined by the equation y=\frac{1}{2}x^{2}-5x+\frac{19}{2}.

Q: Consider the parabola y=ax^2+bx+c, where a, b, and c are constants. (a) Determine the vertex form…

A: (a) Vertex Form of the Parabola:The vertex form of the parabola  is:where (h, k) is the vertex of…

Q: Find the center, transverse axis, vertices, foci, and the asymptote of the y^2-x^2-4x+4y-1=0

A: Steps and explanations are as follows: In case of any doubt, please let me know. Thank you.

Q: Graph the hyperbola 16x^2−32x−4y^2−24y−84=0, noting the center, vertices, cover-tices, and foci.

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Q: Find the focus and directrix of the parabola with the equation 6y^2+10x=0. Then choose the correct…

A: Given that, the equation of the parabola is 6y2+10x=0 6y2+10x=06y2=-10xy2=-10x6y2=-4512x Compare the…

Q: Can you do a parabola with the starting point being (0,0)

A: Given a parabola with equation y=x2

Q: An equation of a parabola is given. y^(2)=8x-2 (a) Find the vertex, focus

A:

Q: Find the equation of the axis of symmetry of the parabola given by y= x^2 - 4 - 45 Explaining your…

A: For a quadratic equation with standard form as y=ax2+bx+c, the axis of symmetry is x=-b2a.

Q: The center of the geometric figure described by 16x^2-160x+36y+292=0 is at what point?

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Q: For the hyperbola given by (9x^2)- (4y^2) -36x -24y - 36 = 0, find the distance between its…

A:

Q: state the center, vertices, equations of asymptotes, and the foci of the following equation x^2/9 -…

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Q: Write an equation of the ellipse in standard form ((x-h)/a)^2 + ((y-k)/b)^2 =1

A: Standard form of ellipse isx-h2a2+y-k2b2=1