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Consider the following statements in respect of circles $x^{2}+y^{2}-2 x-2 y=0$ and $x^{2}+y^{2}=1
1. The radius of the first circle is twice that of the second circle.
2. Both the circles pass through the origin. Which of the statements given above is/are correct?
Options:
1. The radius of the first circle is twice that of the second circle.
2. Both the circles pass through the origin. Which of the statements given above is/are correct?
Solution:
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Verified Answer
The correct answer is:
Neither 1 nor 2
The equation of first circle is $x^{2}+y^{2}-2 x-2 y=0$.
Radius $=\sqrt{(-1)^{2}+(-1)^{2}}=\sqrt{2}$
and equation of second circle is $x^{2}+y^{2}=1$.
Radius $=1$
From above it is clear that the radius of first circle is not twice that of second circle.
$\therefore$ Statement 1 is not correct.
Also, first circle passes through the origin while second circle does not pass through the origin. Hence, neither 1 nor 2 statement is correct.
Radius $=\sqrt{(-1)^{2}+(-1)^{2}}=\sqrt{2}$
and equation of second circle is $x^{2}+y^{2}=1$.
Radius $=1$
From above it is clear that the radius of first circle is not twice that of second circle.
$\therefore$ Statement 1 is not correct.
Also, first circle passes through the origin while second circle does not pass through the origin. Hence, neither 1 nor 2 statement is correct.
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