[填空题]
The diagram below shows : qa8db:vq(yenp( ,qfhmj1 a1 the tr39 e gkxe ooei6)qd 2qk(0bs0ravel path of the Orange Star cargo ship from an aerial vieerodbi 0e 20e(ogq)3kxqs 9k 6w.
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.
