Choose the incorrect statement about the two circles whose equations are given below :
x2 + y2 $-$ 10x $-$ 10y + 41 = 0 and
x2 + y2 $-$ 16x $-$ 10y + 80 = 0
Solution
S<sub>1</sub> $\equiv$ x<sup>2</sup> + y<sup>2</sup> $-$ 10x $-$ 10y + 41 = 0<br><br>Centre C<sub>1</sub> $\equiv$ (5, 5), radius r<sub>1</sub> = 3<br><br>S<sub>2</sub> $\equiv$ x<sup>2</sup> + y<sup>2</sup> $-$ 16x $-$ 10y + 80 = 0<br><br>Centre C<sub>2</sub> $\equiv$ (8, 5), radius r<sub>2</sub> = 3<br><br>Distance between centres = 3<br><br>Hence both circles pass through the centre of each other, have two intersection point and distance between two centres in average of radii of both the circles.<br/><br/>
Hence, option (d) is the incorrect statement.
About this question
Subject: Mathematics · Chapter: Circles · Topic: Equation of a Circle
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