For the line 3x + 2y = 12 and the circle x^2 | vedclass

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(C) The equation of the circle is $x^2 + y^2 - 4x - 6y + 3 = 0$. Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -2$

Vedclass · Accepted Answer

Line is a diameter of the circle

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(C) The equation of the circle is $x^2 + y^2 - 4x - 6y + 3 = 0$. Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -2$ and $f = -3$. The centre of the circle is $(-g, -f) = (2, 3)$. Now,check if the line $3x + 2y = 12$ passes through the centre $(2, 3)$ by substituting the coordinates: $3(2) + 2(3) = 6 + 6 = 12$. Since the line satisfies the equation,it passes through the centre of the circle. Therefore,the line is a diameter of the circle.

For the line $3x + 2y = 12$ and the circle $x^2 + y^2 - 4x - 6y + 3 = 0$,which of the following statements is true?

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