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Chapter 11: Q. 173E (page 1134)

In the following exercises, a). Write the equation in standard form and b). graph.

9y2-x2+18y-4x-4=0

Short Answer

Expert verified

Part (a) The equation of hyperbola isy+121-x+229=1

Part (b) The graph is

Step by step solution

01

Part (a) Step 1. Given information

The equation is 9y2-x2+18y-4x-4=0.

Write the equation in standard form of hyperbola and draw the graph.

02

Part (a) Step 2. Write the equation in standard form of hyperbola 

Simplify the equation.

9y2-x2+18y-4x-4=09y2+2y-x2+4x=4

Covert the equation in complete square

9y2+2y+1-x2+4x+4=4+9-49y+12-x+22=9

Divide the equation by 9 to get standard form of hyperbola

9y+129-x+229=99y+121-x+229=1

03

Part (b)  Step 1. Find centre and asymptote.

In the equation is y+121-x+229=1

They2 term is positive, the transverse axis is vertical.

The hyperbola opens up and down.

Find the centre

Compare the equation with standard form y-k2a2-x-h2b2=1

So, h,k=-2,-1 and a2=1鈬�a=卤1also b2=9鈬�b=卤3

The rectangle that goes through the points 1 units above/below the centre. 3 units left/right of centre.

04

Part (b) Step 2. Draw the graph.

Sketch the asymptotes and draw the graph.

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