Graph transformation

Question

The graph of 9x^2+36x+16y^2-128y+148=0 will undergo a transformation.

a. Write the standard form of this equation.

b. If this equation is translated 3 units right and 5 units down, what is the new equation in standard form?

c. Graph the new equation

Thank you so much!

Answer 1

a)

9x^2+36x+16y^2-128y+148=0

9(x^2+4x)+16(y^2-8y)+148=0

9(x^2+4x+4-4)+16(y^2-8y+16-16)+148=0

9((x+2)^2-4)+16((y-4)^2-16)+148=0

9((x+2)^2)-36+16((y-4)^2-256+148=0

9((x+2)^2)+16((y-4)^2-144=0

9((x+2)^2)+16((y-4)^2=144

Divide each side by 144

9((x+2)^2)/144+16((y-4)^2/144=1

(x+2)^2/16+(y-4)^2/9=1

Answer 2

b)

(x+2)^2/16+(y-4)^2/9=1

x is translted 3 units right and y is translted 5 units down.

 

(x-(-2+3))^2/16+(y-(4-5))^2/9=1

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

Answer 3

C)

Graph of the ellipse