Question

In the system shown below, what are the coordinates of the solution that lies in quadrant I?

x^2+y^2=25
x+y=25

i stink at conic sections so can someone help me?

Answer 1

looks something like this to me

Answer 2

hmm that looks like there are 2 intersecting points though :/

Answer 3

there might be 2 points, cant guarentee that my sketch is accurate tho

Answer 4

since x+y = 25

we know that y = -x+25

insert that "value" of y into the first equation and solve for x

Answer 5

ok so then that would be x^2-x+25=25 correct?

Answer 6

hmm

x^2 + (25-x)^2 = 25

x^2 + x^2 - 50x + 625 = 25

Answer 7

x^2 + x^2 - 50x + 625 = 25

2x^2 - 50x + 600 = 0

2(x^2 =25x + 300) = 0

x^2 =25x + 300 = 0

Answer 8

.... -25 that is :)

Answer 9

x^2 - 25x + 300 = 0

had to edit a typo ;)

Answer 10

ok that makes more sense lol im like: uhhh what? when you put down x^2=25x+300=0 lol

Answer 11

visually, i dont see an intersection; but you might wanna keep at the mathing to verify

http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%3D25%2C+x%2By%3D25

Answer 12

hmm.... maybe if i check with another open study person. @Mertsj ?

Answer 13

y=25-x
\[x^2+(25-x)^2=25\]
\[x^2+625-50x+x^2=25\]
\[2x^2-50x+600=0\]
\[x^2-25x+300=0\]

Answer 14

Can you solve that quadratic equation?

Answer 15

So if you solve the quadratic equation I posted, you will find that the discriminant is negative which means there are no real solutions.

Answer 16

well then why the heck does the question ask me to and i do quote: Write your answer in the form (a,b) without using spaces?

Answer 17

And so the given line does not intersect the given circle in the first quadrant or anywhere else. Perhaps you have posted the equation of the line incorrectly.

Answer 18

ah crap i did write it wrong its supposed to be x^2-y^2=25 and x+y=25 *facedesk*

Answer 19

So you have been given the equation of a hyperbola, not a circle.

Answer 20

So just use the solution I posted but change the signs.

Answer 21

*facekeyboard* sorry about that lol

Answer 22

change the sings? so instead of it being x^2-25+300 its now x^2+25+300=0?

Answer 23

signs*

Answer 24

\[x^2-(25-x)^2=25\]
\[x^2-(625-50x+x^2)=25\]
\[x^2-625+50x-x^2=25\]
\[50x-625=25\]
\[50x=650\]
\[x=13\]
\[y=25-13=12\]
(13,12)

Answer 25

double checked it and its right!! thanks mertsj!

Answer 26

and thank you tcarrol010 for showing me that i plugged in the wrong equation lol

Answer 27

yw