SOLUTION: (x-2)^2/9+(y-3)^2/36=1 y= -1/2x+4 the first equation needs to be written so that it has a y=

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: (x-2)^2/9+(y-3)^2/36=1 y= -1/2x+4 the first equation needs to be written so that it has a y=      Log On


   

Question 436202: (x-2)^2/9+(y-3)^2/36=1
y= -1/2x+4
the first equation needs to be written so that it has a y=
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(x-2)^2/9+(y-3)^2/36=1
y= -1/2x+4
the first equation needs to be written so that it has a y=
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Sub for y in the 1st eqn and multiply thru by 36
4%2A%28x-2%29%5E2+%2B+%28-x%2F2+%2B+1%29%5E2+=+36
4x%5E2+-+16x+%2B+16+%2B+x%5E2%2F4+-+x+%2B+1+=+36
16x%5E2+-+64x+%2B+64+%2B+x%5E2+-+4x+%2B+4+=+144
17x%5E2+-+68x+%2B+68+=+144
17x%5E2+-+68x+-+76+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 17x%5E2%2B-68x%2B-76+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-68%29%5E2-4%2A17%2A-76=9792.

Discriminant d=9792 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--68%2B-sqrt%28+9792+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-68%29%2Bsqrt%28+9792+%29%29%2F2%5C17+=+4.910427500436
x%5B2%5D+=+%28-%28-68%29-sqrt%28+9792+%29%29%2F2%5C17+=+-0.910427500435996

Quadratic expression 17x%5E2%2B-68x%2B-76 can be factored:
17x%5E2%2B-68x%2B-76+=+%28x-4.910427500436%29%2A%28x--0.910427500435996%29
Again, the answer is: 4.910427500436, -0.910427500435996. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+17%2Ax%5E2%2B-68%2Ax%2B-76+%29

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x+=+2+-+12sqrt%2817%29%2F17
y+=+3+%2B+6sqrt%2817%29%2F17
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x+=+2+%2B+12sqrt%2817%29%2F17
y+=+3+-+6sqrt%2817%29%2F17