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Question

Choose the incorrect statement about the two circles whose equations are given below:

x2+y210x10y+41=0and x2+y216x10y+80=0.


A

Distance between two centers is the average radii of both the circles.

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B

Circles have two intersection points.

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C

Both circles’ centers lie inside the region of one another.

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D

Both circles pass through the center of each other.

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Solution

The correct option is C

Both circles’ centers lie inside the region of one another.


Explanation for the correct option:

Step1. Given equations of the circles :

given equation of the circles

x2+y210x10y+41=0.........(1)andx2+y216x10y+80=0..........(2)

Compared with the general equation of the circle

x2+y2+2gx+2fy+c=0

whose center is (-g,-f)and radius is g2+f2-c .

then the center of the circle (1) C1=(5,5)and the center of the circle (2) C2=(8,5)

the radius of the circle (1) r1=52+52-41=9=3 and radius of the circle (2) r2=82+52-80=9=3

Step 2. Check the position of the centers of both circles:

The position ofC1=(5,5) in circle (2)

=25+258050+80=0

The position ofC2=(8,5) in circle (1)

=64+258050+41=0

Thus, both circles’ centers lie inside the region of one another.

Hence, the correct option is (C).


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