SOLUTION: Solve: x^2+y^2=16 x^2/25 + y^2/16 =1 (a) no solutions (b) [(0, -1), (0,4)] (c) [(0, -5), (0,5)] (d) [(-5, 0), (5, )]

Algebra ->  College  -> Linear Algebra -> SOLUTION: Solve: x^2+y^2=16 x^2/25 + y^2/16 =1 (a) no solutions (b) [(0, -1), (0,4)] (c) [(0, -5), (0,5)] (d) [(-5, 0), (5, )]      Log On


   

Question 30338: Solve:
x^2+y^2=16
x^2/25 + y^2/16 =1
(a) no solutions
(b) [(0, -1), (0,4)]
(c) [(0, -5), (0,5)]
(d) [(-5, 0), (5, )]
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i believe that the answer is b) except you have written the answer incorrectly.

+x%5E2+%2B+y%5E2+=+16+ and +%28x%5E2%2F25%29+%2B+%28y%5E2%2F16%29+=+1

+x%5E2+%2B+y%5E2+=+16+
+y%5E2+=+16+-+x%5E2+. Sub this into the second equation, to give:

+%28x%5E2%2F25%29+%2B+%28%2816+-+x%5E2%29%2F16%29+=+1+
+%28x%5E2%2F25%29+%2B+%2816%2F16%29+-+%28x%5E2%2F16%29+=+1+
+%28x%5E2%2F25%29+%2B+1+-+%28x%5E2%2F16%29+=+1+
+%28x%5E2%2F25%29+-+%28x%5E2%2F16%29+=+0+
+-9x%5E2%2F400+=+0+
--> +x%5E2+=+0+
so x = 0.

If x=0, then from +y%5E2+=+16+-+x%5E2+, we get +y%5E2+=+16+-+0%5E2+
--> +y%5E2+=+16+
--> +y+=+sqrt%2816%29+ or +y+=+-sqrt%2816%29+

so, y = 4 or -4.

The 2 solutions are (0,4) and (0,-4).

Check in the second equation, +%28x%5E2%2F25%29+%2B+%28y%5E2%2F16%29+=+1

using (0,4):
+%280%5E2%2F25%29+%2B+%284%5E2%2F16%29+
+0+%2B+%2816%2F16%29+
which is indeed 1... correct.

using (0,-4):
+%280%5E2%2F25%29+%2B+%28%28-4%29%5E2%2F16%29+=+1
+0+%2B+%2816%2F16%29+=+1
which is also 1... correct

jon.