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Chapter 10: Q 62. (page 655)

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

Center at (1,2): focus at(1,4): contains the point(2,2)

Short Answer

Expert verified

The equation of the ellipse is (x-1)21+(y-2)25=1and graph of the ellipse is

Step by step solution

01

. Given information. 

Center at (1,2): focus at (1,4)contains the point(2,2).

Since the center and the focus lie on the line x=1, thus the major axis is parallel to the y-axis.

The distance of the center from one of the foci is c=2

Since, the point (2,2)lies on the ellipse

(2-1)2b2+(2-2)2a2=1b2=1

02

Step 2. The equation of ellipse. 

Substitute c=2and a=1we get.

b2=a2-c2a2=b2+c2a2=1+4a2=5

The equation of the ellipse is(x-1)21+(y-2)25=1

03

Step 3. Graph of the ellipse .    

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Most popular questions from this chapter

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)

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

Foci at(1,2)and(-3,2): vertex at(-4,2).

In Problems 27鈥�34, find two different parametric equations for each rectangular equationy=x3

Prove that the hyperbola

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has the two oblique asymptotesy=abxandy=-abx

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

localid="1647365908255" x2+4xy+y2-3=0
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