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Find the centre and radius of the circle 2x^{2}+2y^{2}-x = 0

Question

Find the centre and radius of the circle $2 x^{2} + 2 y^{2} - x = 0$

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Find the centre and radius of the circle

2 x^{2} + 2 y^{2} - x = 0

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Text solutionVerified

Given

2 x^{2} + 2 y^{2} - x = 0

\Rightarrow (2 x^{2} - x) + 2 y^{2} = 0

\Rightarrow 2 [(x^{2} - \frac{x}{2}) + y^{2}] = 0

\Rightarrow {x^{2} - 2 x (\frac{1}{4}) + (\frac{1}{4})^{2}} + y^{2} - (\frac{1}{4})^{2} = 0

\Rightarrow (x - \frac{1}{4})^{2} + (y - 0)^{2} = (\frac{1}{4})^{2}

which is of the form

(x - h)^{2} + (y - k)^{2} = r^{2}

where

h = \frac{1}{4}

k = 0

and

r = \frac{1}{4}

Thus the centre of the given circle is

(\frac{1}{4}, 0)

while its radius is

\frac{1}{4}

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Question Text	Find the centre and radius of the circle $2 x^{2} + 2 y^{2} - x = 0$
Answer Type	Text solution:1
Upvotes	150