Holiday Problems (1 Viewer)

[mrbassman]

I have holiday revision and there are a couple of problems i cannot do so any help would be greatly appreciated thanks.

Q1/

100 students participated in a survey of sports they are involved with. Of the 100 students, 34 play tennis, 23 play soccer and 31 play basketball. 12 play both tennis and soccer, 6 play both basketball and soccer and 8 play both tennis and basketball. 2 students play all three sports. one student is chosen at random.
What is the probability that he/she plays:
a) at least one sport
b) only one sport

Q2/

Find the equations of the tangents to the parabola

x^2 = 8y

at points A(-4,2) and B(8,8). Find Q, the point of intersection of these tangents. Find the midpoint M of AB and show that the line MQ is parallel to the axis of the parabola.

Q3/

Find the equation of the locus of a point moving so that it is equidistant from the x-axis and the point (-2,-3)

Any help would be great thankyou.

 

[evilc]

hey, here are my solutions, hope they are correct
good luck

 

[evilc]

here is the first one

 

[evilc]

here is the second half btw the last answer is 72/100

 

[Xayma]

Or for the third one, since you know it is equidistant from a point and the line, the locus is a parabola, the focus the point and the line the directix

Ie (x+2)²=-4(y+1.5)

 

[evilc]

Originally posted by Xayma
Or for the third one, since you know it is equidistant from a point and the line, the locus is a parabola, the focus the point and the line the directix

Ie (x+2)²=-4(y+1.5)

yep that is a much quicker and nicer way to do it.

 

[KeypadSDM]

Originally posted by mrbassman
Q3/

Find the equation of the locus of a point moving so that it is equidistant from the x-axis and the point (-2,-3)

Can you assume it's a parabola? Don't you have to derive it from the y=f(t), x=g(t) equations?

 

[evilc]

Re: Re: Holiday Problems

Originally posted by KeypadSDM
Can you assume it's a parabola? Don't you have to derive it from the y=f(t), x=g(t) equations?

I'm not sure if you could assume it and get full marks...it is easy to derive it though

 

[KeypadSDM]

Re: Re: Re: Holiday Problems

Originally posted by evilc
I'm not sure if you could assume it and get full marks...it is easy to derive it though

True, I did assume a little in the 3 unit exam, it cost me

 

[mrbassman]

thanks a lot for your help

 

[Xayma]

Re: Re: Re: Re: Holiday Problems

Originally posted by KeypadSDM
True, I did assume a little in the 3 unit exam, it cost me

I dont know if you need to prove it, it would probably be quicker to use the distance formula then.

It had it in my prelim textbook that it would form a parabola so I have no idea.