From a point P on a rectangular hyper hyperbola at A and B. Show that the a constant, independent of the position F

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

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Q: The following hyperbola has a vertical transverse axis: (x+2)² (+7) _ =1. 17 16

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Q: directrix is x=2 and has a focus at (4,9).

A: Here we apply distance of any point of parabola from directrix and focus is same. We took a general…

Q: Find an equation of the parabola with focus (-2,-5) and directrix y=3

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Q: A parabola is defined by the equation y=x2+2x+3. Write equations of the tangents to the parabola…

A: Given the equation of parabola:

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

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Q: Assuming you know the coordinates of the key points (vertex, foci, directrix), explain how to graph…

A: In the question it is asked to graph conic section assuming vertex, foci, directrix.

Q: State whether the equation x² + ()² + 6z² = 1 defines O a hyperboloid of two sheets. O a paraboloid…

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Q: Find an equation for the parabola with focus (0, -4) and directrix y =

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Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: Find an equation for the hyperbola whose transverse axis is horizontal, with center at (1, -5) and…

A: Given problem:- Find an equation for the hyperbola whose transverse axis is horizontal, with center…

Q: Find the acute angle between the asymptotes of the hyperbola 2x2 –y2 +4x -6y -15 = 0.

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Q: variable circle through the origin and touching the hyperbola xy = c

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Q: Which equation represents a parabola with focus (2, 6) and directrix y = 2? A. y+4=(x-2)² 10 B.…

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Q: Find an equation for the hyperbola that has vertices  (±3,0) and asymptotes  y=±5x.

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

Q: Write the equation for a parabola with a Focus (4,1) and Directrix y=8 ?

A: we know that the distance between any point on parabola and the focus is same as the distance…