Please show all work!! (a) Use implicit differentiation to find the equation of

Question

Please show all work!!

(a) Use implicit differentiation to find the equation of the tangent line to the circle x^2 + y^2 = 169 at (x,y) = (12,5). (b) Use the tangent line to estimate the value y > 0 so that (12.2, y) lies on the circle. (c) Set x = 12.2 and solve the equation x^2 + y^2 = 169 to find the value of y > 0 so that (12.2, y) lies on this circle. Use a calculator to compute a decimal approximation that is correctly rounded to 3 decimal places. (d) Why is the difference between your answers to part b) and c) small?

Explanation / Answer

(a) x^2 + y^2=169

or, 2xdx+2ydy=0

or, dy/dx=-x/y= -12/5

Now the equation of tangent line, 5y+12x=c

at(12,5), c=169

therefore euation of tangent line 5y+12x=169

(b)5y+12x=169

Now when x=12.2 then y=(169-12*12.2)/5=4.52

(c) x^2 +y^2 =169

when x=12.2 then y=4.489

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