lf $g^{2} < c < f^{2}$ then the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ intersects

the coordinate axes

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the x - axis but not the y - axis

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the y - axis but not the x- axis

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None of these

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Solution

The correct option is B the y - axis but not the x- axis
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
For the points of intersection with the y-axis , $x = 0$ . On substituting we get,
$y^{2} + 2 f y + c = 0$
$Δ = 4 (f^{2} - c) > 0$ Hence, there will be two points of intersection with the y-axis.
For the points of intersection with the x-axis, $y = 0$ . On substituting we get,
$x^{2} + 2 g x + c = 0$
$Δ = 4 (g^{2} - c) < 0$ . Hence, there will be no point of intersection with the x-axis.

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Similar questions

The circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ does not intersect x-axis, if

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

What is the condition for the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ to cut the x-axis at more than one point.

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