[填空题]
The diagram below shows the travel path of the Orange Stfvn7 9v4mpz. p2d 5g ljswp+d1ar cargo ship*sz k 67-**ssthg 3ebveck/ss k7+qel from an aerial vie*3+7czk q6ehs/-kk *t*l bses s7vsegw.
The travel path of the Orange Star can be modelled by the quadratic equation
$y=-\frac{x^{2}}{12}+\frac{35 x}{2}, x \geq 0, y \geq 0$
where x and y represent the distance, in kilometres, due east and north from a port located at O(0,0) , respectively. The ship stops at a port located at \mathrm{P}(180,450) for refuelling before continuing its journey.
There is another port located at a point $\mathrm{C}(120,900) $.
1. Determine whether the Orange Star cargo ship passes through port $\mathrm{C}$ . Give a reason for your answer.
2. 1. Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$=-$\frac{x}{a}$+$\frac{b}{c}$;a= .b= ,c= .
2. Hence determine whether port C is the point furthest north on the travel path between the ports O and P . Give a reason for your answer.
3. 1. Find the midpoint of the line segment O P ; M=_( , )
2. Find the gradient of the line segment O P ;M$_{op}$=_( , )
Another cargo ship, The Black Pearl, departs from a new point B(0,100) and travels along a straight path that is parallel to the line segment O P .
4. Find the equation of the Black Pearl's travel path. Express your answer in the form a x+b y+d=0 , where a, b and d $\in \mathbb{Z}$ .
5. Find the coordinates of the point where the Black Pearl's travel path crosses the Orange Star's travel path for a second time.
