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silverxx
 2 years ago
find the tangents of the curve x^2 + y^2  6x + 4y = 0 from (17, 7) the answers are 2x + 3y + 13 and 34x + 129y = 325
silverxx
 2 years ago
find the tangents of the curve x^2 + y^2  6x + 4y = 0 from (17, 7) the answers are 2x + 3y + 13 and 34x + 129y = 325

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myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You can find y'? I think you mean find the tangent of the curve at (17,7), right? You can verify that point is on the circle by pluggin it in.

naranjja
 2 years ago
Best ResponseYou've already chosen the best response.0\[x^2+y^26x+4y=0\]Deriving implicitly,\[2x+2y*y'6+4*y'=0\]\[2y*y'+4*y'=2x+6\]\[y'(2y+4)=2x+6\]\[y'=\frac{ 2x+6 }{ 2y+4 }\]Evaluating at the point (17,7),\[y'=\frac{ 2(17)+6 }{2(7)+4 }=\frac{ 28 }{ 18 }=\frac{ 14 }{ 9 }\]This is the slope. Now, using pointslope form,\[y7=\frac{ 14 }{9 }(x+17)\]\[y=\frac{ 14 }{ 9 }x+\frac{ 301 }{ 9 }\]And that is the tangent that goes through that point.

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0yes dy/dx = 2x+6/2y + 4

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2hmmm...I don't think that point in on the circle.

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0@naranjja you missed 2x + 6.. i think. the sign

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0@myininaya i don't know.. hmm

naranjja
 2 years ago
Best ResponseYou've already chosen the best response.0\[y'=\frac{ 2x+6 }{ 2y+4 }\]\[y'=\frac{ 2(17)+6 }{ 2(7)+4 }=\frac{ 40 }{ 18 }=\frac{ 20 }{ 9 }\]Therefore,\[y7=\frac{ 20 }{ 9 }(x+7)\]\[y=\frac{ 20 }{ 9 }x+\frac{ 203 }{ 9 }\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You want to find the tangent to the curve at (17,7) That point isn't on the circle. Or do you want to find a tangent line to a point on the circle that goes through that point?

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0you think it'll satisfy the answers?? it was written in the book hehe

naranjja
 2 years ago
Best ResponseYou've already chosen the best response.0And I wrote 7 instead of 17, my bad:\[y7=\frac{ 20 }{ 9 }(x+17)\]\[y=\frac{ 20 }{ 9 }x+\frac{ 403 }{ 9 }\]

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0@naranjja there are 2 answers hehe

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Is there anymore info given in the problem? Like the yintercepts of the lines?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Oh! Do you mean find the tangent points? And those are the lines that are given in the problem?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2"find the tangents of the curve x^2 + y^2  6x + 4y = 0 from (17, 7) the answers are 2x + 3y =13 and 34x + 129y = 325" So we have 2x+3y=13 34x+129y=325 Put both into y=mx+b form. :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You guys already found the general slope m=y'=(x+3)/(y+2)

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0i need to find the process in order to reach the correct answers

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0find's not the term but to solve

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Right. We are trying to find the tangent points. I'm telling you how to get there.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You need to put both of those lines that were given into y=mx+b form.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2And is that one line 2x+3y=13?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2I think it is because (17,7) has to be on it. Ok so you find the slopes of both of those lines. Set it equal to the general slope of the curve you guys found. And solve both equations.

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0wait.. my solution's 2x+6/ 2y+4 = y7/ x 17

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2So we have 2x+3y=13 34x+129y=325 I'm asking you to put both of those into y=mx+b form so we can identify the slopes of the tangent lines.

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0got 2y^2 + 2x^2  40x  10y + 79

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0i think i have my own way to solve this..

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0but i was just too stupid in not deriving the answers

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2look I will do the first one for you it isn't hard We have 2x+3y=13 Solve for y 3y=2x13 y=2x/313 Slope is 2/3 So this means 2/3=(x+3)/(y+2) Remember (x+3)/(x+2) is what you guys found above. I just reduced the fraction. Solve for x and y. 2=x+3 3=y+2 You should get point on a circle. More importantly the tangent point that is on the line 2x+3y=13 that goes through (17,7).

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2But actually I could be wrong...ERRR...That result isn't on the circle. Let me think a little more.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2oh it is i just don't know how to add :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2So that is one point. You can find the other using that same process.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2With the other line that was given to you.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.234x + 129y = 325 So first step is to write this into y=mx+b form Identify the slope. Put y'=m and solve for x and y to find the other tangent point.

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0okay. i'll try it later.. i think i need to digest this..

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You should get a result that isn't even on the circle. However you could find another tangent point whose line that goes through (17,7) by looking at my workings from above.

silverxx
 2 years ago
Best ResponseYou've already chosen the best response.0thank thank thank you so much @myininaya :))

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You can get another tangent point by looking at this: 2/3=(x+3)/(y+2) I did 2=x+3 , 3=y+2 You have also looked at it as 2/3=(x+3)/(y+2) which means you could solve 2=x+3 and 3=y+2 to find the other point.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2But okay. I understand. Have fun.
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