Find an equation for the sphere centered at (1, -2, 3) containing the origin. V14 = x + y+ z 14 = x? + y? + z? V14 = (x – 1)? + (y + 2)² + (z – 3)² - 14 = (x – 1)? + (y+2)² + (z – 3)² | V14 = /(x – 1)2 + (y+2)² + (z – 3)²

Q: Write the equation of the hyperbola 25x? – 9y? + 100x + 72y – 269 = 0 in standard form (z – h)? (y –…

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Q: Describe the yz-intercept of the sphere with the equation x2 + y2+z2 - 2x+ 10z +5 = 0

A: The given equation of sphere is: x2+y2+z2-2x+10z+5=0

Q: 4x2+y2-16y+8y+16=0 Identify the conic section by rewriting it in standard graphing form.

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Q: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is  4x+2y2+8=0

Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

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

Q: 1. A parabola has equation -12x + y? – 24 = 0. Write the equation in standard form.

A: The equation of the parabola is, - 12x + y² - 24 = 0 So, y² = 12x + 24

Q: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: (0,7) (12,14) (20,0), create a parabolic model H(x) in the standard form H(x)=ax+bx+c for the path…

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Q: 11. Write the equation of the conic section in standard form. 7x² – 3y² – 70x –12y+142 =0

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Q: 42 - 8r - 16,

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Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

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.