3x2 5y2 12x 30y 42 0 a Rewrite into standard form b How

3x^2 + 5y^2 -12x + 30y + 42 = 0 a.) Rewrite into standard form b.) How long is the major axis?

Solution

7.   3x²+5y² -12x +30y+42=0

     3(x²-4x) +5(y²-6y) + 42=0

      3(x²-4x +4-4) + 5(y²-6y + 9 -9)+42=0

       3(x-2)² + 5(y-3)²-12 -45+42=0

      (x-2)²/5   +   (y-3)²/3=1

Here a²=5

a=sqrt5

Length of major axis=2a=2sqrt5