What is the centre of the equation 4x^2 9y^2 - 32x 36y 11
2 answers
There is addition sign b/n 4x^2 + 9y^2
I think you mean the center of the ellipse whose equation is (assuming the blanks represent + signs):
4x^2 + 9y^2 - 32x + 36y + 11 = 0
4x^2-32x + 9y^2+36y + 11 = 0
4(x^2-8x) + 9(y^2+4y) = -11
now complete the squares and add the same amounts on the right side:
4(x^2-8x+16) + 9(y^2+4y+4) = -11+4(16)+9(4)
4(x-4)^2 + 9(y+2)^2 = 89
center is at (4,-2)
If I got the original equation wrong, fix it and follow the same steps.
4x^2 + 9y^2 - 32x + 36y + 11 = 0
4x^2-32x + 9y^2+36y + 11 = 0
4(x^2-8x) + 9(y^2+4y) = -11
now complete the squares and add the same amounts on the right side:
4(x^2-8x+16) + 9(y^2+4y+4) = -11+4(16)+9(4)
4(x-4)^2 + 9(y+2)^2 = 89
center is at (4,-2)
If I got the original equation wrong, fix it and follow the same steps.