1. Okay, you got the equation x^2 = y^2 - 4

If x = 0, what is y = p = ? Replace in the equation above.

If x = 5, what is y = t = ? Replace in the equation above

As for getting the greatest possible slope, consider this. The equation for slope is:

m = (y2-y1)/(x2-x1)

Now, I already got the values of x fixed. What's left is the denominator, and to achieve the greatest possible slope, I need to get the highest possible value in the denominator. Suppose that y2 = ħa and y1 = ħb, the highest value would be:

y2 - y1 = (+a) - (-b) = a + b