matematikk.net

linja l : x=t ^ y=k+2t

sirkel : x^2 + (y-3)^2 = 25

bestem k, slik at l tangerer sirkelen

Linja l: y[sub]l[/sub] = k + 2x

og sirkelen s: y[sub]s[/sub] = 3 [symbol:plussminus] [symbol:rot] (25 - x[sup]2[/sup])

Deriverer disse og y[sub]l[/sub] = y[sub]s[/sub] ):

[tex]y_l^,\,=\,2\,\text \,og\,\,y_s^,\,=\,\frac{-x}{\sqrt{25-x^2}[/tex]

[tex]y_l^,\,=\,y_s^,\;\;[/tex]gir

[tex]x^2\,=\,4(25\,-\,x^2)[/tex]

): x = [symbol:plussminus] 2 [symbol:rot] 5

setter inn etc:

[tex]y\,=\,3 \pm \sqrt{5}\,=\,k\,\mp 4\sqrt{5}[/tex]

som gir:

[tex]k\,=\,3\,\pm\,5\sqrt{5}[/tex]