Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

Question

anonymous · Answer

original trajectory: y=6x+2

anonymous · Answer

PLEASE HELP!!!

danjs · Answer

hi

anonymous · Answer

hey,wats up? :)

danjs · Answer

So there is going to be a point where that line crosses the elipse

anonymous · Answer

yea i just dont know how to put my original trac. into the new problem? any ideas?

danjs · Answer

yeah...

danjs · Answer

put y = 6x+2 into the circle equation

danjs · Answer

|dw:1419487653020:dw|

anonymous · Answer

i am going to send to what i had got, give me a minute

danjs · Answer

ok, ill start typing out stuff

anonymous · Answer

y2+x2=40000 ,y=6x+2
6x2+2+x2=40000
7x2+2=40000
7x2=39998
I get stuck here.

danjs · Answer

$$(6x+2)^2 +x^2 = 40000$$
$$[36x^2 + 24x + 4] + x^2 = 200^2$$
$$37x^2 + 24x - 39996 = 0$$

danjs · Answer

remember you are squaring a quantity 
(a +b)^2 = a^2 +2ab + b^2

danjs · Answer

see that?

anonymous · Answer

ohh, okay so  that's were i went wrong.

danjs · Answer

$$Ax^2 + Bx^2 + C = 0$$
$$x = \frac{ -B \pm \sqrt{B^2 - 4*A*C} }{ 2*A }$$

anonymous · Answer

okay finna plug hem in an solve

anonymous · Answer

i mean them,lol

danjs · Answer

yep

danjs · Answer

ill start typing it up while you work at it

danjs · Answer

$$x = \frac{ -24 \pm \sqrt{24^2 - 4*37*(-39996)} }{ 2*37 }$$

$$x = \frac{ -24 \pm \sqrt{5919984} }{ 74 }$$

$$x = \frac{ -24 \pm 84\sqrt{839} }{ 74 } = \frac{ -24 }{ 74 } \pm \frac{ 84\sqrt{839} }{ 74 }$$

$$x = \frac{ 12 }{ 37 } \pm \frac{ 42\sqrt{839} }{ 37 }$$

$$x \approx 32.56 ~~or~~x \approx -33.20$$

anonymous · Answer

sorry, but i have to leave. emergency!!! This seems shaddy, and im sorry. thanks for all of your help though :)

danjs · Answer

the question is shady? lol.

anonymous · Answer

Shaddy...

danjs · Answer

FOr the future, 
Use those 2 x values in the equation for the line, and get the 2 y values, those are your two intersection points.

anonymous · Answer

:)