hey
can someone help me with this question
thanks 
Hey! Let me run you through the processes for each. The first bit, we know two coordinates, \((0,-6)\) and \((5,-1)\). So we can substitute to form two equations:
You can solve those simultaneously
for Part (ii), we know the x-coordinate is \(\alpha\), so let's substitute that into the equation (with the h and k we now have) and we'll get a y-coordinate:
That y-coordinate we just found is actually the HEIGHT of the rectangle (but we ignore a negative if there is one) - The width is \(2\alpha\). Why? The function we are examining is even, so if Q is at \(\alpha\), then P is at \(-\alpha\). PQ is therefore \(2\alpha\)!
So the area is:
From this, I reckon \(h=30\) and \(k=5\) to match the statement in the question
Right, so we are working with the function they give in Part (iii).
To find a maximum, we differentiate (quotient rule):
-120\alpha^2}{\left(\alpha^2+5\right)^2})
Now put it equal to zero:
)
Then you test that with a point either side check as usual - Then pop it back into the area formula
Note: Did this quickly, subject to computational errors.
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