Alan

Convert r = 2 / (7sinθ-cosθ) to rectangular form.

Enter your answer in slope-intercept form

Well, given a and b we can write   

As follows:

If the curve is continuous then we must have:

At x = 2:   a*2 + 3 = 2 - 5  or 2a = -6   so a = -3

At x = -2:  2*(-2) - b = -2 - 5   or  -4 - b = -7  so  b = 3

I get the following:

Let  x = 0.51010101010....

10x = 5.1010101010....

1000x = 510.1010101010....

1000x - 10 x = 505

990x = 505

x = 505/990 = 101/198

Here's a ittle more help:

Now differentiate k with respect to \(\theta\) , set to zero and solve for \(\theta\)  Select the solution that gives a value for k leading to the maximal area.

Here's a bigger hint:

As follows:

(The other two solutions are ≈ -0.975 and 3.203)