a.a.) x² + y² - 4x - 2y - 31 = 0

Pusat = - \frac{A}{2} , -\frac{B}{2} = -\frac{-4}{2} , -\frac{-2}{2} = (2 , 1)−

2

A

,−

2

B

=−

2

−4

,−

2

−2

=(2,1)

Jari-Jari = √A² + B² - C

= √2² + 1² - (-31)

= √4 + 1 + 31

= √36

= 6

b.Jawaban

pusat dan jari-jari lingkaran begin mathsize 14px style 2 x squared plus 2 y squared minus 20 x plus 12 y plus 10 equals 0 end style adalah begin mathsize 14px style open parentheses 10 comma space minus 6 close parentheses space dan space 3 square root of 4 end style.

Pembahasan

Pusat dan jari-jari lingkaran begin mathsize 14px style L identical to x squared plus y squared plus A x plus B y plus C equals 0 end style ditentukan dengan rumus:

Pusat = begin mathsize 14px style open parentheses negative A over 2 comma space minus B over 2 close parentheses end style

Jari-jari = begin mathsize 14px style square root of A squared over 4 plus B squared over 4 minus C end root end style

Sehingga dapat diperoleh pusat dan jari-jari lingkaran begin mathsize 14px style 2 x squared plus 2 y squared minus 20 x plus 12 y plus 10 equals 0 end style adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row Pusat equals cell open parentheses negative fraction numerator open parentheses negative 20 close parentheses over denominator 2 end fraction comma negative 12 over 2 space close parentheses end cell row blank equals cell open parentheses 10 comma space minus 6 close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell Jari minus jari end cell equals cell square root of open parentheses negative 20 close parentheses squared over 4 plus 12 squared over 4 minus 10 end root end cell row blank equals cell square root of 400 over 4 plus 144 over 4 minus 10 end root end cell row blank equals cell square root of 126 end cell row blank equals cell 3 square root of 4 end cell end table end style

Jadi, pusat dan jari-jari lingkaran begin mathsize 14px style 2 x squared plus 2 y squared minus 20 x plus 12 y plus 10 equals 0 end style adalah begin mathsize 14px style open parentheses 10 comma space minus 6 close parentheses space dan space 3 square root of 4 end style.