Question?

[Guest]

At how many points do the graphs of
x^2 + y^2 = 9
and
x^2/4 + y^2/36 = 1
intersect?

a. 0
b. 1
c. 2
d. 3
e. 4 THIS RIGHT?
f. None of these

 

[stapel]

Doing a quick sketch, yes, it looks like you've picked the correct option.

Eliz.

 

[Guest]

By letting each of these equations equal each other will allow you to find the common points...

x^2 + y^2 = 9

and

x^2/4 + y^2/36 = 1

x^2 + y^2/ 9 = 4

and use your (x^2) = 9 - y^2 in the above equation an solve for y...

 

[soroban]

Hello, adam40g!

At how many points do the graphs of .\(\displaystyle x^2\,+\,y^2\:=\:9\) .and .\(\displaystyle \frac{x^2}{4}\,+\,\frac{y^2}{36}\:=\:1\) .intersect?

. . . a. 0 . . . b. 1 . . . c. 2 . . . d. 3 . . . e. 4 . . . f. None of these

I believe you're expected to recognize the two conic equations.

If you sketch the curves as Eliz suggested, the answer is clear.

\(\displaystyle x^2\,+\,y^2\:=\:9:\) a circle centered at the origin with radius 3.

\(\displaystyle \frac{x^2}{4}\,+\,\frac{y^2}{36}\:=\:1:\) an ellipse centered at the origin with intercepts \(\displaystyle (\pm2,\,0)\) and \(\displaystyle (0,\,\pm6)\)

You are correct . . . (e) 4