For the four circles M,N,O and P, following four equations are given: Circle M:x^2+y^2=1 Circle N:x^2+y^2-2x=0 Circle O:x^2+y^2-2x-2y+1=0 Circle…
JEE Main 2021 — Mathematics Coordinate Geometry
2021mcqhard
For the four circles M,N,O and P, following four equations are given:
Circle M:x2+y2=1
Circle N:x2+y2−2x=0
Circle O:x2+y2−2x−2y+1=0
Circle P:x2+y2−2y=0
If the centre of circle M is joined with centre of the circle N, further centre of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a
Official previous-year question
Held on 18 Mar 2021 · Verified 6 Jul 2026.
Options
A
Rhombus
B
Square
C
Rectangle
D
Parallelogram
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Solution
M:x2+y2=1center=(0,0)
N:x2+y2−2x=0,center=(1,0)
O:x2+y2−2x−2y+1=0,center=(1,1)
P:x2+y2−2y=0,center=(0,1)
MN=(1−0)2+(0−0)2=1
NO=(1−1)2+(0−1)2=1
OP=(1−0)2+(1−1)2=1
PM=(0−1)2+(1−1)2=1
Then, all the sides are equal of a quadrilateral then MNOP is a square.
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