Mohon Bantuannya Kak Jawab Soal Matematika Saya Kak .... Question from @ahmad536399

ahmad536399 @ahmad536399

July 2022 1 19 Report

Mohon Bantuannya Kak Jawab Soal Matematika Saya Kak

zuhdim106

a. mencari titik pusat dan jari-jari L₁

x² + y² - 6x - 2y + 6 = 0

P₁ ( -½A, -½B ) = [ -½(-6), -½(-2) ] = ( 3, 1 ) = ( x₁, y₁ )

$r = \sqrt{( - \frac{1}{2}a) {}^{2} + ( - \frac{1}{2}b) {}^{2} - c } \\ = \sqrt{3 {}^{2} + 1 {}^{2} - 6 } \\ = \sqrt{9 + 1 - 6} \\ = \sqrt{4}$

R₂ = 2

mencari titik pusat dan jari-jari L₂

x² + y² + 10x + 4y + 20 = 0

P₂ ( -½A, -½B ) = ( -½.10, -½.4 ) = ( -5, -2 ) = ( x₂, y₂ )

$r = \sqrt{( - \frac{1}{2}a) {}^{2} + ( - \frac{1}{2} b) {}^{2} - c} \\ = \sqrt{( - 5) {}^{2} + ( - 2) {}^{2} - 20} \\ = \sqrt{25 + 4 - 20} \\ = \sqrt{9}$

R₁ = 3

Mencari jarak pusat( P₁ P₂ )

( P₁ P₂ )² = ( x₂ - x₁ )² + ( y₂ - y₁ )²

= ( -5 - 3 )² + ( -2 - 1 )²

= (-8)² + (-3)²

= 64 + 9

= 73

P₁ P₂ = √73

Mencari GSPD

GSPD² = ( P₁ P₂ )² - ( R₁ + R₂ )²

= ( √73 )² - ( 3 + 2 )²

= 73 - 5²

= 73 - 25

= 48

GSPD = √48

= 4√3 satuan

Mencari GSPL

GSPL² = ( P₁ P₂ )² - ( R₁ - R₂ )²

= ( √73 )² - ( 3 - 2 )²

= 73 - 1

= 72

GSPL = √72

= 6√2 satuan

b. mencari titik pusat dan jari-jari L₁

x² + y² - 4x - 8y - 5 = 0

P₁ ( -½A, -½B ) = [ -½(-4), -½(-8) ] = ( 2, 4 ) = ( x₁, y₁ )

$r = \sqrt{( - \frac{1}{2} a) {}^{2} + ( - \frac{1}{2} b) {}^{2} - c) } \\ = \sqrt{2 {}^{2} + 4 {}^{2} + 5} \\ = \sqrt{4 + 16 + 5 } \\ = \sqrt{25}$

R₁ = 5

mencari titik pusat dan jari-jari L₂

x² + y² - 2y + 6y + 6 = 0

P₂ ( -½A, -½B ) = ( -½(-2), -½.6 ) = ( 1, -3 ) = ( x₂, y₂ )

$r = \sqrt{( - \frac{1}{2}a) {}^{2} + ( - \frac{1}{2} b) {}^{2} - c } \\ = \sqrt{1 {}^{2} + ( - 3) {}^{2} - 6 } \\ = \sqrt{1 + 9 - 6} \\ = \sqrt{4}$

R₂ = 2

mencari titik pusat( P₁ P₂ )

( P₁ P₂ )² = ( x₂ - x₁ )² + ( y₂ - y₁ )²

= ( 1 - 2 )² + ( -3 - 4 )²

= (-1)² + (-7)²

= 1 + 49

= 50

P₁ P₂ = √50

= 5√2

Mencari GSPD

GSPD² = ( P₁ P₂ )² - ( R₁ + R₂ )²

= ( 5√2 )² - ( 5 + 2 )²

= 25.2 - 7²

= 50 - 49

= 1

GSPD = √1

= 1 satuan

Mencari GSPL

GSPL² = ( P₁ P₂ )² - ( R₁ - R₂ )²

= ( 5√2 )² - ( 5 - 2 )²

= 25.2 - 3²

= 50 - 9

= 41

GSPL = √41 satuan

c. mencari titik pusat dan jari-jari L₁

x² + y² - 2x - 4y + 1 = 0

P₁ ( -½A, -½B ) = ( -½(-2), -½(-4) ) = ( 1, 2 ) = ( x₁, y₁ )

$r = \sqrt{( - \frac{1}{2}a) {}^{2} + ( - \frac{1}{2}b) {}^{2} - c } \\ = \sqrt{1 {}^{2} + 2 {}^{2} - 1 } \\ = \sqrt{1 + 4 - 1} \\ = \sqrt{4}$

R₂ = 2

mencari titik pusat dan jari-jari L₂

x² + y² + 8x - 10y + 32 = 0

P₂ ( -½A, -½B ) = ( -½.8, -½(-10) ) = ( -4, 5 ) = ( x₂, y₂ )

$r = \sqrt{( - \frac{1}{2}a) {}^{2} + ( - \frac{1}{2} b) {}^{2} - c } \\ = \sqrt{( - 4) {}^{2} + 5 {}^{2} - 32 } \\ = \sqrt{16 + 25 - 32} \\ = \sqrt{9}$