Write the equations of the two asymptotes?

Question

Graph (y+3)2/9 - (x-2)2/16 = 1

Part I: Identify the coordinates of the center of this hyperbola.

center = (2,-3)

Part II: Use the values of a or b to locate the coordinates of the vertices.
=(2,-3,-3) , ( 2,-3+3)
=(2,-6) , (2,0)

Part III: What are the coordinates of the foci?
=(2,-3 + or  - sqrt 16+9 )
= ( 2, -3 + or - 5)
= (2,-8) , (2,2)
Part IV: Write the equations of the two asymptotes.

I need help with part 4 please!!

Elizabeth M · Answer

Replace the 1 by zero  and you get (y+3)/3=(x-2)/4 and (y+3)/3= -(x-2)/4
which are the equations of the asymptotes.

Pope · Answer

Incidentally, the first three parts seem to check out well.

The vertical (y-direction) radius is 3. The horizontal (x-direction) radius is 4. The slopes of the asymptotes are -3/4 and +3/4. Both asymptotes must include the center, so work from point-slope form.

y + 3 = -3/4(x - 2)
4y + 12 = -3x + 6
3x + 4y + 6 = 0

y + 3 = 3/4(x - 2)
4y + 12 = 3x - 6
3x - 4y - 18 = 0

Write the equations of the two asymptotes?

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