Find the fractional form of this equation

Question

16x²+7y²-64x-48=0

Answer 1

16x² - 64x + 7y² = 48

 

Complete the square on the x terms:

 

16(x²-4x+4) + 7y² = 48 + 16·4

16(x-2)² + 7y² = 112

 

Divide by 16·7 (=112):

 

(x-2)²/7 + y²/16 = 1

 

This is the equation of an ellipse centered at (2,0).