(B) The given equation of the circle is $x^2 + y^2 + 6x - 8y + 9 = 0$.Comparing this with the general equation $x^2 + y^2 + 2gx + 2fy + c = 0$,we get

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(B) The given equation of the circle is $x^2 + y^2 + 6x - 8y + 9 = 0$.Comparing this with the general equation $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = 3$,$f = -4$,and $c = 9$.The length of the intercept made by the circle on the $x$-axis is given by $2\sqrt{g^2 - c}$.Substituting the values,we get $2\sqrt{3^2 - 9} = 2\sqrt{9 - 9} = 0$.Since the intercept on the $x$-axis is $0$,the circle touches the $x$-axis.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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For the circle $x^2 + y^2 + 6x - 8y + 9 = 0$,which of the following statements is true?

A
Circle passes through the point $(-3, 4)$
B
Circle touches $x$-axis
C
Circle touches $y$-axis
D
None of these

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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For the circle $x^2 + y^2 + 6x - 8y + 9 = 0$,which of the following statements is true?

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If the radical axis of the circles $x^2 + y^2 - 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ forms a triangle of area $A$ with the coordinate axes,then the value of $\frac{1}{A}$ is

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