Can someone explain how to do the please:
The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the trajectory , y=2x+4, in complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

Question

Can someone explain how to do the please: 
The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the trajectory , y=2x+4, in complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

anonymous · Answer

your idea?

anonymous · Answer

I have no clue. I know first you would have to make sure they are both in slope intercept but idk how to get the first one into slope intercept form

anonymous · Answer

Oh wait or can you solve it a different way without graphing

anonymous · Answer

ok, reply if you got me, please
the orbit of the Earth is a circle with the radius is $\sqrt40000=200$|dw:1405124128417:dw|

anonymous · Answer

Okay.. I get what you did there

anonymous · Answer

the trajectory of the ship is y = 2x+4 |dw:1405124206184:dw|

anonymous · Answer

when the ship "meets" the orbit, the ship is in both the trajectory and the orbit, right?

anonymous · Answer

|dw:1405124359461:dw|

anonymous · Answer

I understand so far

anonymous · Answer

so, you just plug y = 2x+4 to y^2 +x^2 =40000 to solve for x, then plug that x back into y = 2x+4 to solve for y.
the result (x,y) is where the ship meets the orbit

anonymous · Answer

Okay just give me a sec to solve and make sure I understand. Thanks, I appreciate you being so detailed

anonymous · Answer

:)

anonymous · Answer

Sorry but I'm having trouble solving. I plugged it back in and got this far$$8x ^{2}+16x+16=40000$$
I think im doing something wrong

anonymous · Answer

y = 2x+4 --> y^2 =(2x+4)^2 = 4x^2+16x+16 . that's y^2 only
now y^2 +x^2 =40000
replace y^2 above 4x^2 +16x+16+x^2 =40000
simplify 5x^2 +16x+16 =40000 while your equation is 8x^2+..... which is not right

anonymous · Answer

Ohhh I see what I did. So now would I subtract 16 from 4000 then divide by 16x? Im still left with 16x^2

anonymous · Answer

Determinant?

anonymous · Answer

http://www.purplemath.com/modules/quadform.htm

anonymous · Answer

I am sorry, discriminant, I misuse with determinant in linear algebra

anonymous · Answer

Can I use the $$b ^{2}-4ac $$ even though this is not set equal to zero

anonymous · Answer

why not?? 5x^2 +16x+16=40000 
minus both sides by 40000, you have 5x^2 +16x -39984=0

anonymous · Answer

then apply b^2 -4ac

anonymous · Answer

Oh...Ive just never had a number that big haha. Thank you