Alpha particles are deflected along hyperbolic paths when they are directed towards the nuclei of gold atoms. If an alpha particle gets as close as 33 units to the nucleus along a hyperbolic path (where the nucleus is at 3 -x, 11 the center of the hyperbola) with asymptote y what is the equation of its path? Assume that it's a hyperbola that opens left and right.

Q: -X 4 Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at…

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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: 13. Which of the following is the equation of the graph shown? 2 Parabola Oy = - 3x? – 6x – 2 Oy = -…

A: The objective is to find the equation of the graph.

Q: 4. A parabola has focus F( 11, 8) and directrix x= -17. Find its standard equation

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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: Write the equation of a parabola in standard form from the given information Vertex at (2, -2)…

A: Vertex of the parabola is at 2, -2 and focus at 2, -3. Now vertex is, h, k=2, -2⇒h=2  &  k=-2…

Q: 8. Find the equation of the conic whose focus is (4, -5) and directrix is x = -2.

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Q: An object is observed travelling in a hyperbolic trajectory with the sun at one focus of the…

A: Given information:  1. Sun is one of the focus of hyperbola . 2. The Sun co-ordinate is 0,0.…

Q: suppose that a non periodic comet will visit the solar system with the sun located at the focus of…

A: Parabolic trajectory of comet is 16y - 24 = x2. and sun located at its focus while earth at the…

Q: The center of the ellipse with the given equation 4(x – 5)² + 3(y – 4)2 = 48 is %3D (-5, 4) (4, 5) O…

A: Solving the problem by finding the centre in standard form.

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

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Q: Write the equation of a circle passing through the vertices of the hyperbola 4x2-9y2=36 and having a…

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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.

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.