Easy MCQ +4 / -1 PYQ · JEE Mains 2021

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

  1. A Distance between two centres is the average of radii of both the circles.
  2. B Both circles pass through the centre of each other.
  3. C Circles have two intersection points.
  4. D Both circle's centers lie inside region of one another. Correct answer

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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