Question

The chord of contact (1,2) with respect to the circle
x2 + y2 - 4x - 6y + 2 = 0) is
18+ y - 6=0 2x+2y-2=0
3) 2x +y+6=0
4) not existing​

Answer 1

Answer:

1 , 2

Step-by-step explanation:

Hope it will help you

Answer 2

The chord of contact (1,2) with respect to the circle x^2 + y^2 - 4x - 6y + 2 = 0 is 1) 18+ y - 6=0, 2) 2x+2y-2=0 ,3) 2x +y+6=0 4) not existing​.

Option 4) Not existing is the correct answer.

Given:

Circle equation = x² + y² - 4x - 6y + 2 = 0  and point(1,2)

To Find:

The chord of contact (1,2) with respect to the circle x² + y² - 4x - 6y + 2 = 0 .

Solution:

Given Circle equation - x² + y² - 4x - 6y + 2 = 0

The general Equation of circle is  x² + y² + 2gx + 2fy + c = 0

On comparing both the equations,

∴ g = -2 , f = -3 and c=2

Equation of chord of contact is

$xx_{1} +yy_{1} + g(x+x_{1} ) +f(y+y_{1} ) + c=0\\\\(x_{1},y_{1}) =(1,2)$

⇒ 1*x+2*y -2(x+1) -3(y+2) + 2=0

⇒ x + 2y -2x -2 -3y -6 +2 =0

⇒ -x -y -6 = 0

∴ x+ y+ 6 = 0

Given options doesn't have the above option.

∴ Option 4) Not existing is the correct answer.

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