SOLUTION: 1)if the line 3x+4y+k=0 touches the ellipse 9x2 +16y2=144 find the value of k 2)x-y=5 touches the ellipse whose foci are +-3,0 find the eq of ellipse 3)find the eq of ellipse pas

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 1)if the line 3x+4y+k=0 touches the ellipse 9x2 +16y2=144 find the value of k 2)x-y=5 touches the ellipse whose foci are +-3,0 find the eq of ellipse 3)find the eq of ellipse pas      Log On


   

Question 331736: 1)if the line 3x+4y+k=0 touches the ellipse 9x2 +16y2=144 find the value of k
2)x-y=5 touches the ellipse whose foci are +-3,0 find the eq of ellipse
3)find the eq of ellipse passing through pt 2,-3 and touching the line x-2y+8=0
4)find k if y=x+k touches the ellipse 2x2 + 3y2=1
5)find the eq of tangent from -2,-1 to an ellipse 2x2 + 3y2 =6
6)prove that x+3 root y=9 is a tangent to an ellipse x2/9+y2/4=1 also find the pt of contact.
i am unable to solve these problem please help me solve it.i have test in tution today.want the solutin today itself.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1)if the line 3x+4y+k=0 touches the ellipse 9x2 +16y2=144 find the value of k
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The slope of the line is -3/4.
The slope of the ellipse is -9x/16y
Find the 2 points where -9x/16y = -3/4
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-9x/16y = -3/4
y = 3x/4
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Sub for y in 9x%5E2+%2B+16y%5E2+=+144
9x%5E2+%2B+16%289x%5E2%2F16%29+=+144
18x%5E2+=+144
x = ± sqrt(8)
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16y%5E2+=+144+-+72+=+72
y = ± 3sqrt(2)/2
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The 2 points are (2sqrt(2),3sqrt(2)/2) and (-2sqrt(2),-3sqrt(2)/2)
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Use y = mx + b and the points to find b, and then k.
3sqrt(2)/2 = (-3/4)*(2sqrt(2)) + b
b = 3sqrt(2)
y = (-3/4)x + 3sqrt(2)
3x + 4y = 12sqrt(2)
k = -12sqrt(2)
k = +12sqrt(2)