Choose the incorrect statement about the two circles whose equations are given below: x2+y2-10 x-10 y+41=0 and x2+y2-16 x-10 y+80=0

Question

Choose the incorrect statement about the two circles whose equations are given below: x2+y2-10 x-10 y+41=0 and x2+y2-16 x-10 y+80=0 (A) Distance between two centres is the average of radii of both the circles (B) Both circles' centres lie inside region of one another (C) Both circles pass through the centre of each other (D) Circles have two intersection points

Tardigrade Admin · Accepted Answer

r 1=3, c 1(5,5) r 2=3, c 2(8,5) C 1 C 2=3, r 1=3, r 2=3 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/b744534328d1a90cf93ec27faf61ed91-.png" />

Q. Choose the incorrect statement about the two circles whose equations are given below:
$x^{2} + y^{2} - 10 x - 10 y + 41 = 0$ and $x^{2} + y^{2} - 16 x - 10 y + 80 = 0$

Distance between two centres is the average of radii of both the circles

Both circles' centres lie inside region of one another

Both circles pass through the centre of each other

Circles have two intersection points

$r_{1} = 3, c_{1} (5, 5)$
$r_{2} = 3, c_{2} (8, 5)$
$C_{1} C_{2} = 3, r_{1} = 3, r_{2} = 3$

Q. 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