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samnatha
 2 years ago
find the value of K for which x + 4y + K = 0 is a tangent to x^2 + y^2  2x + 2y  15 = 0
samnatha
 2 years ago
find the value of K for which x + 4y + K = 0 is a tangent to x^2 + y^2  2x + 2y  15 = 0

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campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0you need to find the point(s) of contact before you can find K you could solve simultaneously and finding the 1 point of contact between the curve and the tangent. Substitution seems the most obvious method. An alternative method is to differentiate and let the derivative equal the slope of the tangent (1/4) then solve for x.. once you know x find y by substituting. When you have the point of contact substitute into the tangent equation and solve for K

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0i tried your first method and subed in 4y  k for x i then got a big long equation that went like this 17y^2 + K^2 + 8yk + 2K + 10 y = 0

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0ok because you are dealing with a circle then there are 2 points where the the tangents can occur dw:1354733396218:dw so rewrite theequation as 2 parts \[y = \sqrt{17  (x 1)^2}  1... and ....y =  \sqrt{17  (x1)^2} 1\] differentiate both of those.... let the derivatives equal 1/4 and solve for x.

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0we have not done differentiate yet so i have no idea how to do it that way

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0ok.... that makes it difficult..

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0yeah it does how would i do it the other way do u know ?
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