The equation x2-y2-2 x-4 y - 5-0 representsA- none of theseB- a pointC- a circle of non-zero radiusD- a pair of straight lines

The correct option is B a point The radius of the given circle =√(1^2+( 2)^2 5)=0 Hence, the radius of the given circle is zero, which represents a point. ...

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Standard XII

Mathematics

Obtaining Centre and Radius of a Circle from General Equation of a Circle

The equation ...

Question

The equation $x^{2} + y^{2} + 2 x - 4 y \times 5 = 0$ represents

a point

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a pair of straight lines

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a circle of non-zero radius

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none of these

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Solution

The correct option is A
a point

The radius of the given circle

$= \sqrt{1^{2} + (- 2)^{2} - 5} = 0$

Hence, the radius of the given circle is zero, which represents a point.

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Similar questions

Q. The equation x² + y² + 2x − 4y + 5 = 0 represents
(a) a point
(b) a pair of straight lines
(c) a circle of non-zero radius
(d) none of these

Q. The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x² − y² −2x + 4y − 3 = 0, is
(a) x² + y² − 2x − 4y + 4 = 0
(b) x² + y² + 2x + 4y − 4 = 0
(c) x² + y² − 2x + 4y + 4 = 0
(d) none of these

The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines
$x^{2} - y^{2} - 2 x + 4 y - 3 = 0,$ is

Q. The equation

25 [x^{2} + y^{2} - 2 x + 1] = (4 x - 3 y + 1)^{2}

represents

Q. The equation

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

represents

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The equation x2+y2+2x−4y×5=0 represents

The correct option is A a point The radius of the given circle =√12+(−2)2−5=0 Hence, the radius of the given circle is zero, which represents a point.

The equation $x^{2} + y^{2} + 2 x - 4 y \times 5 = 0$ represents

The correct option is A
a point

The radius of the given circle

$= \sqrt{1^{2} + (- 2)^{2} - 5} = 0$

Hence, the radius of the given circle is zero, which represents a point.