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Crap Adobe Digital Ed. ab Docs Adobe Reader X abMedia avast! Free Antivirus abPhoto Google Chrome Acer Remote iTunes Files Inbox x Homewo x M Mathwa x ACS C https:// www.mathway.com 24.1.2 11 of 19 complete Ex. Score: 0 of 6 pts HW Score: 46% (46 of 100 pts) Heat flows normal to isotherms, curves along which the temperature is constant. Find the line along which heat flows through the point (3,4) when the isotherm is along the graph of GO 34 The equation of the line along which heat flows is y ysMenu dll und OK Enter your answer in the answer box, then click Check Answer All parts showing Clear All Check Answer Save 10:48 AM 4/15/2015

Explanation / Answer

2x^2 + y^2 = 34

Deriving implciitly :

4x + 2yy' = 0

4x = -2yy'

y' = -4x / (2y)

y' = -2x / y

Plug in point (3,4), we get :

y' = -2(3) / 4

y' = -3/2

So, what we have found above is the slope of tangent line

So, slope of normal line is -1 / y'

m =-1 / (-3/2)

m = -1 * (-2/3)

m = 2/3

So, slope = 2/3 and point is (3,4)

y - y1 = m(x - x1)

y - 4 = (2/3)(x - 3)

y - 4 = (2/3)x - 2

y = (2/3)x - 2 + 4

y = (2/3)*x + 2 ----> ANSWER

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