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Chapter 10: Q 13. (page 699)

In Problems 11鈥�18, find an equation of the conic described. Graph the equation by hand

Ellipse; foci at (-3,0)and (3,0); vertex at(4,0)

Short Answer

Expert verified

The Equation of the ellipse isx216+y27=1

Step by step solution

01

Step 1. Given Information

Foci at (-3,0),(3,0)

Vertex at(4,0)

02

Step 2. Calculation

Since (h+c,k)=(-3,0)(h-c,k)=(3,0)

and (h+a,k)=(4,0)

Hence h=0,c=-3,k=0&a=4

Then b2=a2-c2=16-9=7

Then the equation is

x216+y27=1

03

Step 3. Graph

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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 the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at0,2and its vertex at0,0.

Prove that the hyperbola

y2a2-x2b2=1

has the two oblique asymptotesy=abxandy=-abx

Answer Problems using the figure.

The coordinates of the vertex are_______ .

The distance dfrom P1=(2,-5)to P2=(4,-2)is d=________.
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