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xxTIMURxx [149]
3 years ago
14

Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

Mathematics
1 answer:
borishaifa [10]3 years ago
8 0
Implicit defferentation

remember that dy/dx y= dy/dx


so
take derivitive of both sides
2x+2y \space\ \frac{dy}{dx}=0
solve for \frac{dy}{dx}
minus 2x both sides
2y \space\ \frac{dy}{dx}=-2x
divide both sides by 2y
\frac{dy}{dx}=\frac{-2x}{2y}
\frac{dy}{dx}=\frac{-x}{y}

when is the slope equal to \frac{5}{12}
solve for \frac{dy}{dx}=\frac{5}{12}
\frac{dy}{dx}=\frac{5}{12}
\frac{5}{12}=\frac{-x}{y}
5y=-12x
y=\frac{-12}{5}x
find where the circle and this line intersects

substitute \frac{-12}{5}x for y
x^2+(\frac{-12}{5}x)^2=676
x^2+\frac{144}{25}x^2=676
\frac{25}{25}x^2+\frac{144}{25}x^2=676
\frac{169}{25}x^2=676
times both sides by \frac{25}{169}
x^2=100
sqrt both sides, take positive and negative roots
x=+/-10

sub back

y=\frac{-12}{5}x
y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)
y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}
y=-24 \space\ or \space\ 24

the points are (10,-24) and (-10,24)
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