A circle which touches the positive axes- and whose centre it at distance 2 -2 from the origin- then the equation is

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Equation of Circle with Origin as Center

A circle whic...

Question

A circle which touches the positive axes, and whose centre it at distance $2 \sqrt{2}$ from the origin, then the equation is

x²+y²+4x+4y=0

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x²+y²+4x+4y+2=0

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x²+y²- 4x-4y+4=0

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Solution

The correct option is D
x²+y²- 4x-4y+4=0

Let O and C be the origin nad the centre of the circle respectively.
C = (r,r)
OC = $2 \sqrt{2} \Rightarrow O C^{2}$ = 8
C = (2,2,) r = 2 $\Rightarrow 2 r^{2}$ = $8 \Rightarrow r^{2}$ = $4 \Rightarrow r$ = $2$
$(x - 2)^{2} + (y - 2)^{2}$ = $2^{2} \Rightarrow x^{2} + y^{2} - 4 x - 4 y + 4$ = 0

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A circle which touches the positive axes, and whose centre it at distance 2√2 from the origin, then the equation is

The correct option is D x 2+y2 - 4x-4y+4=0 Let O and C be the origin nad the centre of the circle respectively. C = (r,r) OC = 2√2⇒OC2 = 8 C = (2,2,) r = 2 ⇒2r2 = 8⇒r2 = 4⇒r = 2 (x−2)2+(y−2)2 = 22⇒x2+y2−4x−4y+4 = 0

A circle which touches the positive axes, and whose centre it at distance $2 \sqrt{2}$ from the origin, then the equation is