Need help please!!?

Question

x^2 + y^2 =144

x^2 -4y^2 =64

can someone help me figure out the formula for this, everything I have done so far has been wrong.

Answer 1

You need to solve for one variable in both equations, then substitute so that you only have one variable. Then it gets easy.
Working with the first equation:

x^2 + y^2 = 144

y^2 = 144 - x^2

You just reworded one equation in terms of y^2. Now, do the same thing for the other one.

x^2 - 4y^2 = 64

-4y^2 = 64 - x^2

y^2 = (64 - x^2) / -4

Now, that you have both equations equal to the same thing (y^2), you can set them equal to one another.

144 - x^2 = (64 - x^2) / -4

-576 + 4x^2 = 64 - x^2

-576 + 5x^2 = 64

5x^2 = 640

x^2 = 128

x = +/- 11.3137085

Now, substitute this back in for X to solve for Y. You can use either of the original equations.

x^2 + y^2 = 144

(128) + y^2 = 144

y^2 = 16

y = +/- 4

...and that's it! I hope this helped you. Check the equation by substituting the +/-11.3 or the +/-4 back into the original equations...you'll see that it works out. I hope I get best answer, lol.

Answer 2

Here it goes:

you can 'add' both equations in such a way that one of the variables is eliminated, 'x' is simpler because it has '1' as coefficients in both equations.. So:
x^2+y^2=144
(-1)x^2-4y^2=64(-1)

x^2+y^2=144
-x^2+ay^2=-64
----------------------------
5y^2=80
y^2=80/5
y^2=16
y=(+/-) 4

Substitute 4 in one of the above equations:

x^2+(4)^2=144
x^2+16=144
x^2=144-16
x^2=128
x=sqrt128

Factoring this result:

x=sqrt(64*2)
or:
x=(+/-)8sqrt2

So there's the solutions (8sqrt2, 4), (8sqrt2,-4),(-8sqrt2,4) & (-8sqrt2,-4)

Answer 3

x^2 + y^2 =144
This is the equation for a circle with center at origin and radius = 12

x^2 -4y^2 =64
Divide by 64 getting:
x^2/8^2 - y^2/4^2 = 1
This is the equation of a hyperbola with foci on the x-axis and the center at the origin. a + 8, b= 4 and c = sqrt(a^2+b^2)= 16sqrt(5)The foci are located at (c,0) and (-c,0). The vertices are located at (-a,0) and (a,0).

Answer 4

x^2-4y^=64
x^2=64+4y^2...
substitue into 1st eqn

64+4y^2+y^2=144
5y^2=80
y^2=16
y=+/-4

now plug back into either original equation

x^2 +(4)^2=144
x^2+16=144
x^2=128
x=sqrt(128)
x=8*sqrt(2)

Answer 5

substitute u = x^2 and v = y^2

u + v = 144
u - 4v = 64

substracting second from first

u - u + v + 4v = 144 - 64

5v = 80

v = 16
u = 144 - 16 = 128

x = +/- sqrt(u) = +/- 4
y = +/- sqrt(v) = +/- 8 * sqrt(2)

So 4 solutions(4, 8sqrt(2)), (-4, 8sqrt(2)), (4, -8sqrt(2)), (-4, -8sqrt(2))

Answer 6

You haven't told us what your problem is, so we can't tell you the "formula". Be more explicit plz.