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

1. campbell_st

you 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

2. samnatha

i 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

3. campbell_st

ok 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 $y = \sqrt{17 - (x -1)^2} - 1... and ....y = - \sqrt{17 - (x-1)^2} -1$ differentiate both of those.... let the derivatives equal -1/4 and solve for x.

4. samnatha

we have not done differentiate yet so i have no idea how to do it that way

5. campbell_st

ok.... that makes it difficult..

6. samnatha

yeah it does how would i do it the other way do u know ?