Project: S is a surface in R° with equation x² +y² – z² = 1. The point P (2,1,2) lies on this hyperboloid. It turns out there are exactly 2 straight lines L1 and L2 which pass through the point P and lie entirely inside the surface S.

Q: Sketch the parabola, and label the focus, vertex, and directrix.. (a) (y-1)=-12(x+4) (x−1)² = 2(y-2)…

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Q: Write the equation of an ellipse centered at (1, -2) whose minor axis has length 6 and horizontal…

A: We can find the equation of ellipse using the given data as below.

Q: What is the standard form equation of the ellipse that has vertices (-6, 2) and (4, 2) and…

A: vertex  (-6,2) and  (4,2) co vertex (-1,-2)  and  (-1, 6)

Q: One focus of a hyperbola lies at the point (0, -7) and the cor-responding directrix is the line y =…

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Q: Find the equations of the osculating circles of the ellipse 25x2 + 4y? = 100 at the points (2,0) a.…

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Q: 2 y² - x² = 9 a) Sketch the graph of the equations in three dimensions and identify the surfaces.

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Q: The paraboloid z = 8-x-x²-3y2 intersects the plane x = 2 in a parabola. Find parametric equations in…

A: The equation of the paraboloid is given as z=8-x-x2-3y2. The paraboloid intersects the plane x=2 in…

Q: The focus of a parabola is (2, 5) and the directrix is y = 1. What is the equation of the parabola?…

A: Given Focus (2, 5) of a parabola and the directrix y=1We need to find the equation of the…

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.

Q: Determine the line of intersection of the two planes: x+y-z-2=0 and 2x-y+3z-1=0. Write the…

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