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Chapter 10: Q. 37 (page 654)

Find an equation for each ellipse. Graph the equation by hand.

Center at(0,0), vertex at(0,4),b=1

Short Answer

Expert verified

The equation of ellipse is x2+y216=1and the graph is

Step by step solution

01

Step 1. Given Information

We are given vertex at(0,4),b=1

02

Step 2. Calculation

The vertices lie on the y-axis. So, the major axis of the ellipse is y-axis and the vertices formed by minor axis are (1,0)and(-1,0)

Find the value of foci using the formula.

b2=a2-c212=42-c2c2=16-1c2=15

Thus, the equation of ellipse is as follows,

x2b2+y2a2=1x212+y242=1x2+y216=1

On plotting the points on the graph, we get,

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Most popular questions from this chapter

In Problems 31– 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40.4x2-4xy+y2-85x-165y=0

Answer Problem using the figure.

If a = 4, then the coordinates of the focus are___________.

Rutherford’s Experiment In May 1911, Ernest Rutherford published a paper in Philosophical Magazine. In this article, he described the motion of alpha particles as they are shot at a piece of gold foil 0.00004 cm thick. Before conducting this experiment, Rutherford expected that the alpha particles would shoot through the foil just as a bullet would shoot through snow. Instead, a small fraction of the alpha particles bounced off the foil. This led to the conclusion that the nucleus of an atom is dense, while the remainder of the atom is sparse. Only the density of the nucleus could cause the alpha particles to deviate from their path. The figure shows a diagram from Rutherford’s paper that indicates that the deflected alpha particles follow the path of one branch of a hyperbola.

(a) Find an equation of the asymptotes under this scenario.

(b) If the vertex of the path of the alpha particles is 10cm from the center of the hyperbola, find a model that describes the path of the particle.

Find an equation for each ellipse. Graph the equation by hand.

Center at (2,-2): vertex at (7,-2): focus at(4,-2).

The graph of a parabola is given. Match graph to its equation.

and equations of the parabola areA)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)
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