JEE PYQ: Circle Question 4
Question 4 - 2021 (17 Mar Shift 1)
Choose the incorrect statement about the two circles whose equations are given below:
$x^2 + y^2 - 10x - 10y + 41 = 0$ and $x^2 + y^2 - 16x - 10y + 80 = 0$
(1) Distance between two centres is the average of radii of both the circles.
(2) Both circles’ centres lie inside region of one another.
(3) Both circles pass through the centre of each other.
(4) Circles have two intersection points.
Show Answer
Answer: (2)
Solution
$C_1(5,5), r_1 = 3$; $C_2(8,5), r_2 = 3$. Distance $C_1C_2 = 3 = r_1 = r_2$. Each circle passes through the other’s centre. They intersect at two points. But centres don’t lie inside the other circle (distance = radius, on boundary). Statement (2) is incorrect.
BETA
