Question

x^2+y^2=9
16x^2-4y^2=64

Answer 1

If you have an equation that can be written as

x^2/a^2 + y^2/b^2 = 1 (a>=b>0) it is an ellipse (circle is a special case of an ellipse) centred on the origin.

If you have an equation that can be written as

x^2/a^2 - y^2/b^2 = 1 (a,b>0) it is a hyperbola centred on the origin.

Answer 2

solve for real solutions

Answer 3

Ah, you didn't say that:-) If there are real solutions there must be 4 of them (where the arms of the hyperbola cross the ellipse.

Answer 4

what are they though

Answer 5

Let's see, if I work out 1 of them that will give me the other three by symmetry...

Answer 6

ok so whata are all 4 ?

Answer 7

Hmm...multiply that first one by 16 and subtract the second one from it gives 20y^2 = 80 or y= 2.....

Answer 8

Well, plus or minus 2....

Answer 9

so what are all 4

Answer 10

can you type them all out for me

Answer 11

I will, just on the phone...

Answer 12

ok

Answer 13

Huh, just noticed I can divide that second one by 4...duh.

Answer 14

How about (root5, plus or minus 2) and (-root5, plus or minus 2)?

Answer 15

yeah thats right thank you

Answer 16

u r welcome:-)

Answer 17

x*2 +y*2 =9
16x*2 -4y*2 =64 /4 --- 4x*2 -y*2 =16 --- y*2 = 4x*2 -16

x*2 +4x*2 -16 =9
5x*2 =25
x*2 =5
x_1,_2 = +/- radical 5