The line 2x +3y = 1 is tangent to 4x^2 -9y^2 = 19
:
Solve the linear equation for y
:
1) y = -2x/3 +1/3
:
substitute for y in the equation of the hyperbole
:
4x^2 -9(-2x/3 +1/3)^2 = 19
:
4x^2 -9(4x^2/9 -4x/9 +1/9) = 19
:
4x^2 -4x^2 +4x -1 = 19
:
4x -20 = 0
:
4x = 20
:
x = 5
:
use equation 1 to get the value of y
:
y = -2(5)/3 +1/3 = -3
:
******************************************************************
solution is x = 5, y = -3 which is the point (5, -3)
:
check the solution
:
hyperbole
:
4(5^2) -9(-3)^2 = 19
:
100 -81 = 19
:
19 = 19
:
Line
:
2(5) +3(-3) = 1
:
10 -9 = 1
:
1 = 1
Mark as brainlist
