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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
 6 months ago
 6 months 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
 6 months ago
 6 months ago

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myininayaBest ResponseYou've already chosen the best response.2
You 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.
 6 months ago

naranjjaBest 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.
 6 months ago

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

myininayaBest ResponseYou've already chosen the best response.2
hmmm...I don't think that point in on the circle.
 6 months ago

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

silverxxBest ResponseYou've already chosen the best response.0
@myininaya i don't know.. hmm
 6 months ago

naranjjaBest 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,\[y7=\frac{ 20 }{ 9 }(x+7)\]\[y=\frac{ 20 }{ 9 }x+\frac{ 203 }{ 9 }\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
You 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?
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
you think it'll satisfy the answers?? it was written in the book hehe
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
@myininaya the second
 6 months ago

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

silverxxBest ResponseYou've already chosen the best response.0
@naranjja there are 2 answers hehe
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Is there anymore info given in the problem? Like the yintercepts of the lines?
 6 months ago

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

myininayaBest 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. :)
 6 months ago

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

silverxxBest ResponseYou've already chosen the best response.0
i need to find the process in order to reach the correct answers
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
find's not the term but to solve
 6 months ago

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

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

myininayaBest ResponseYou've already chosen the best response.2
And is that one line 2x+3y=13?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
I 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.
 6 months ago

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

myininayaBest ResponseYou've already chosen the best response.2
So 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.
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
got 2y^2 + 2x^2  40x  10y + 79
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
i think i have my own way to solve this..
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
but i was just too stupid in not deriving the answers
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
look 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).
 6 months ago

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

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

myininayaBest ResponseYou've already chosen the best response.2
So that is one point. You can find the other using that same process.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
With the other line that was given to you.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
34x + 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.
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
okay. i'll try it later.. i think i need to digest this..
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
You 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.
 6 months ago

silverxxBest ResponseYou've already chosen the best response.0
thank thank thank you so much @myininaya :))
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
You 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.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
But okay. I understand. Have fun.
 6 months ago
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