Question

4x^2-6y^2+32x-24y+16=0

give the exact coordinated of an four points

Answer 1

(4x^2 +32x +____) -(6y^2 -24y + ____) = 16 +4(__)-6(___)

4(x^2 +8x +16) -6(y^2 -4y +4) = 16 +4(16)-6(4)

Answer 2

4(x+4)^2 -6(y-2)^2 = 16 +64-24

4(x+4)^2 -6(y-2)^2 = 24

4/24(x+4)^2 -6/24(y-2)^2 = 1

(1/6)(x+4)^2 -(1/4)(y-2)^2 = 1

Answer 3

when y=0;

(x+4)^2 = 12

x+4 = +- 4sqrt(3)

x = -4 +- 4sqrt(3)

(-4 + 4sqrt(3),0) (-4 + 4sqrt(3),0) are 2 points

Answer 4

when y = 2;

(x+4)^2 = 6

x = -4 +- sqrt(6)

(-4 + sqrt(6),2) (-4 -sqrt(6),2) are 2 mor epoints

Answer 5

thanks