SOLUTION: The line 3x+4y=15 intersects the curve 2xy=9 at A and B. Find a) the coordinates of A and of B, b) the distance AB

Algebra ->  Coordinate-system -> SOLUTION: The line 3x+4y=15 intersects the curve 2xy=9 at A and B. Find a) the coordinates of A and of B, b) the distance AB      Log On


   



Question 384723: The line 3x+4y=15 intersects the curve 2xy=9 at A and B. Find
a) the coordinates of A and of B,
b) the distance AB

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.3x%2B4y=15
2.2xy=9
From eq. 2,
4y=18%2Fx
Substitute into eq. 1,
3x%2B18%2Fx=15
3x%5E2%2B18=15x
x%5E2-5x%2B6=0
%28x-2%29%28x-3%29=0
Two solutions:
x-2=0
x=2
Then,
2%282%29y=9
y=9%2F4
.
.
.
x-3=0
x=3
Then,
2%283%29y=9
y=3%2F2
.
.
.

.
.
.
Now that you have the coordinate, use the distance formula to find the distance between them.
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
D%5E2=%283-2%29%5E2%2B%283%2F2-9%2F4%29%5E2
D%5E2=1%2B%286%2F4-9%2F4%29%5E2
D%5E2=1%2B%28-3%2F4%29%5E2
D%5E2=1%2B9%2F16
D%5E2=16%2F16%2B9%2F16
D%5E2=%2816%2B9%29%2F16
D%5E2=25%2F16
highlight%28D=5%2F4%29