the equation of a curve is xy=12 and the equation of a line l is 2x+y=k where k is a constant .In the case where k=11 find the c

The equations given are xy=12 and 2x+y=11.

To find the intersection points, you can isolate one of the variables, either x or y, and substitute into the other equation. I’ll choose to express x in terms of y.

Rearranging the first equation for y gives us y=12/x.

Substituting this y value into the second equation leads to an equation with a single variable to solve for x. This results in 2x + 12/x = 11.
To eliminate the fraction, multiply both sides by x, giving...
2x^2 - 11x + 12 = 0.
From here, we can factor to get (2x-3)(x-4).
By setting both factors to zero, we can solve for x values which yields x = 3/2 and x = 4.
Next, we substitute these x values back into the original equation xy=12 to find the corresponding y coordinates. This results in the points:
(3/2, 8) and (4, 3). The curves intersect at these two locations.