The radius of the circle x -5 x -1- y -8 y -4-0 isA- 4 unitsB- 2 -2 unitsC- 3 -2 unitsD- 8 units

The correct option is B 2√(2) unitsEquation nbsp;of the circle is (x 5)(x 1)+(y 8)(y 4)=0 Hence, end points of diameter will be (5,8) and (1,4) ∴ Radius, r=√ ...

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Standard XII

Mathematics

Equation of Circle Whose Extremities of a Diameter Given

The radius of...

Question

The radius of the circle $(x - 5) (x - 1) + (y - 8) (y - 4) = 0$ is

8

units

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4

units

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2 \sqrt{2}

units

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3 \sqrt{2}

units

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Solution

The correct option is C $2 \sqrt{2}$ units
Equation of the circle is $(x - 5) (x - 1) + (y - 8) (y - 4) = 0$
Hence, end points of diameter will be $(5, 8)$ and $(1, 4)$
$∴$ Radius, $r = \frac{\sqrt{(5 - 1)^{2} + (8 - 4)^{2}}}{2}$
$\Rightarrow r = 2 \sqrt{2}$ units

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The radius of the circle (x−5)(x−1)+(y−8)(y−4)=0 is

The correct option is C 2√2 unitsEquation of the circle is (x−5)(x−1)+(y−8)(y−4)=0 Hence, end points of diameter will be (5,8) and (1,4) ∴ Radius, r=√(5−1)2+(8−4)22 ⇒r=2√2 units

The radius of the circle $(x - 5) (x - 1) + (y - 8) (y - 4) = 0$ is

The correct option is C $2 \sqrt{2}$ units
Equation of the circle is $(x - 5) (x - 1) + (y - 8) (y - 4) = 0$
Hence, end points of diameter will be $(5, 8)$ and $(1, 4)$
$∴$ Radius, $r = \frac{\sqrt{(5 - 1)^{2} + (8 - 4)^{2}}}{2}$
$\Rightarrow r = 2 \sqrt{2}$ units