Please will someone talk through this?

Question

anonymous · Answer

talk through what?

anonymous · Answer

Adding the questions now :)

anonymous · Answer

oh ok sorry for interrupting

anonymous · Answer

|dw:1425848475996:dw|

anonymous · Answer

i don't get it.

anonymous · Answer

Figure 2 shows the curve with the equation y^2 = 9(x-1) and the line with the equation 3x+y=9

anonymous · Answer

The curve crosses the x-axis at point A, and the line intersects the curve at the points P and Q
(a) Find the coordinates of point A
(b) Find, using algebra, the coordinates of P and Q

anonymous · Answer

So far I got that, y^2 = 9x-9 so y=3x-3

asnaseer · Answer

HINT: to find point A, you know that along the x-axes we have y=0, so solve:$$y^2=0=9(x-1)$$

anonymous · Answer

attachment

anonymous · Answer

there is a graph...

anonymous · Answer

The one I drew isn't accurate, just a sketch

asnaseer · Answer

@Green101 - use the hint I gave to solve part a)

anonymous · Answer

I got a = (1,0) and I know thanks!!

anonymous · Answer

It is mainly part B I don't understand!!

asnaseer · Answer

great! now for part (b) you know that along the line we have:$$3x+y=9$$$$\therefore y=9-3x$$$$\therefore y^2=(9-3x)^2=81-54x+9x^2$$

asnaseer · Answer

and we know that along the curve we have:$$y^2=9(x-1)=9x-9$$these two equations must be equal at points P and Q

asnaseer · Answer

therefore you need to solve:$$81-54x+9x^2=9x-9$$

asnaseer · Answer

you should be able to rearrange this into a standard quadratic equation in $x$ and then factor it and solve

anonymous · Answer

You are an absolute legend! Thank you so so much! If I post the answer here will you check it??

asnaseer · Answer

sure - and thank you very much for the compliment :)

anonymous · Answer

So far I got that $$x = 5, 2 $$

asnaseer · Answer

perfect! :)

anonymous · Answer

from $$x^2-7x+10=0$$

anonymous · Answer

So what would I do from here to calculate P and Q?

asnaseer · Answer

simplest is to use the equation of the straight line for each x to get the corresponding y value

anonymous · Answer

So, finally I got

anonymous · Answer

$$y=(-3)(5)+9  $$
$$\therefore y=6 < 0 $$ and therefore Q = (5, -6)

asnaseer · Answer

correct co-ordinates for Q but I believe you meant to pu:$$y=-6\lt0$$

asnaseer · Answer

*put

anonymous · Answer

$$y=(-3)(2)+9 $$$$\therefore y=3 > 0$$ and so p = (2,3)

anonymous · Answer

And yeah I did XD

asnaseer · Answer

you have the right answers :)

anonymous · Answer

Yay! Again thank you so much!! Really needed someone to talk through all this!

asnaseer · Answer

yw :)