Convert general form to standard form 4x2 9y2 48x 72y 14

Convert general form to standard form. 4x^2 + 9y^2 - 48x + 72y + 144 = 0 (x - 6)^2/108 + (y + 8)^2/48 = 1 (x - 12)^2/18 + (y + 8)^2/8 = 1 (x - 12)^2/16 + (y + 8)^2/36 = 1 (x - 24)^2/36 + (y - 36)^2/16 = 1 (x - 6)^2/36 + (y + 4)^2/16 = 1

Solution

4x²+ 9y²-48x+72y+144=0

First we have to write the x terms together and y terms together

4x²-48x+9y²+72y+144=0

next we take out the GCF from the x terms and the y terms

4(x²-12x) + 9(y²+8y) +144=0

next is to use completing the square method and write both x and y terms in form of perfect square.

4(x²-12x+36-36)+ 9(y²+8y+16-16) +144=0

4((x-6)²-36) +9((y+4)²-16)+144=0

Next we have to distribute the GCF that is 4 and 9

4(x-6)^2-4(36)+ 9(y+4)²-9(16) + 144=0

4(x-6)²-144 +9(y+4)²-144+144=0

4(x-6)²+9(y+4)²-144=0

Move 144 to the right side

4(x-6)² + 9(y+4)² = 144

Divide both sides by 144

4(x-6)²/144 + 9(y+4)²/144=1

Next step is to reduce the left side

(x-6)²/36 + (y+4)²/16= 1

Hence the correct option is the last option.