If the normal at point P to the rectangular hyperbola x2 - y? = 4 meets the transversal and conjugate axes at A and B respectively and C is the center of the hyperbola, then O PA = PC O PA = PB O AB = 2PC O PB = PC

Q: 2. Sketch the hyperbola y² - 2y - 4x² - 8x - 7 = 0. Find its centre, foci, eccentricity, asymptotes,…

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Q: Consider this hyperbola. 9(x+5)2 - 25(y-2)2 =225 a) find parametric equations to describe the…

A: (a) Rearrange the equation to find the equation of the parabola in the standard form. Then find the…

Q: Which of the following equations represents a parabola with vertex (5,2) and directrix y = - 2? (А)…

A: Let's find equation of parabola.

Q: Identify the vertices and foci of the hyperbola y2 - x2/4 = 1.

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Q: A hyperbola in standard position has equation 36x2 −49y2 −100 = 0. Write down a parametrisation of…

A: The given equation of the hyperbola is: 36x2-49y2-100=0 Rewrite the equation:…

Q: The line through the two foci that also intersects a hyperbola at its two vertices is known as the…

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Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: What must be true of the foci of a hyperbola? The foci must lie --Select--- of the hyperbola and…

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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: After putting the equation into one of the two forms for the parabola, find the focus and directrix…

A: We have the equation of a parabola x2+6x-12y+33=0 We have to find focus and directrix The…

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: State whether the equation z - ()² = (+)² defines a hyperboloid of two sheets. an ellipsoid. a…

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Q: What is the equation of the standard hyperbola with vertices at(0, ±a) and foci at (0, ±c)?

A: Given-  Hyperbola with vertices at (0, ±a) and foci at (0, ±c). To find- The standard equation of…

Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

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Q: Find the standard equation of the hyperbola having vertices at (0,plus or minus 3) and foci at…

A: We know, if the vertices and foci are on the y-axis then the standard equation of the hyperbola is…

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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