Penjelasan dengan langkah-langkah:

Lingkaran x² - 4x + y² +6y = 12

(x - 2)² + (y + 3)² = 12+ 2² + 3²

(x - 2)² + (y + 3)² = 25

titik P(x, y1) = ( 1, 4) diluar lingkaran

garis kutub p --> (x1 - 2)(x - 2) + (y1 + 3)(y + 3) = 25

(1 - 2)(x - 2) + (4 + 3)(y + 3) = 25

- (x - 2) + 7 (y + 3 )= 25

-x + 2 + 7y + 21 - 25 =0

-x + 7y - 2 = 0 atau x - 7y + 2 = 0

atau x = 7y - 2

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cari titik singgung pada lingkaran ,

sub x = 7y - 2 ke (x - 2)² + (y + 3)² = 25

(7y - 2 - 2)² + (y + 3)² = 25

(7y- 4)² + (y + 3)² = 25

49y² - 56y+ 16 + y² + 6y + 9 - 25= 0

50y² - 50 y = 0

50y ( y - 1)= 0

y = 0 atau y = 1

x = 7y - 2

y = 0 --> x = - 2 --> A(-2,0)

y = 1 --> x = 5 ---> B (5, 1)

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garis singgung lingkaran

(x1 - a)(x - a) + (y1 - b)(y - b) = r²

(x1 - 2)(x - 2) + (y1 + 3) (y + 3) = 25

i) A(x1,y1) = (-2,0)

(-2 -2) (x -2) + (0 +3)(y+3) = 25

-4(x - 2) + 3 (y + 3) = 25

-4x + 8 + 3y +9 = 25

-4x + 3y - 8 =0

4x - 3y + 8 = 0

ii) garis singgung melalaui B(5,1)

(5 - 2)(x - 2) + (1 + 3)(y + 3) = 25

3(x - 2) + 4(y + 3) = 25

3x - 6 + 4y + 12 = 25

3x + 4y - 19 = 0