Tolong bantu jawab! persamaan lingkaran(x-2)^2+y^2:16 ditransformasikan oleh matriks (1 0 1 2)di lanjutkan dengan refleksi terhadap sumbu x. tentukan persamaan

jawab

(x - 2)² + y² = 16

T1 = [1..0||1...2]
T2 = [1..0||0..-1]

(x',y') = T2 o T1 (x,y)

[tex] \left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}1&0\\0&-1\end{array}\right] \left[\begin{array}{ccc}1&0\\1&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] [/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right]\,=\, \left[\begin{array}{ccc}1&0\\-1&-2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] [/tex]

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right]\,=\, \frac{1}{-2} \left[\begin{array}{ccc}-2&0\\1&1\end{array}\right] \left[\begin{array}{ccc}x'\\y'\end{array}\right][/tex]

x = x'
y = -1/2 (x' +y')
sub ke  (x -2)² + (y)² = 16

(x' -2)²  + { -1/2 (x' +y')}² = 16
x² - 4x  + 4 + 1/4 (x² + 2xy + y²) = 16
x² + 1/4 x² - 4x + 1/2 xy + 1/4 y² + 4 -16 =0
5/4 x²- 4x + 12 xy + 1/4 y² -12 =0 ....kalikan 4
5x²-16x + 48 xy + y² - 48 = 0