Knockout NEET 2024
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Q.11 Show that the relation R in the set A of points in a plane given by
, is an equivalence relation. Further, show that the set of
all points related to a point is the circle passing through P with origin as
centre.
The distance of point P from origin is always same as distance of same point P from origin i.e.
R is reflexive.
Let i.e. distance of the point P from the origin is same as the distance of the point Q from the origin.
this is same as : distance of the point Q from the origin is same as the distance of the point P from the origin i.e.
R is symmetric.
Let and
i.e. distance of the point P from the origin is same as the distance of the point Q from the origin, and aslo distance of the point Q from the origin is same as the distance of the point S from the origin.
We can say that distance of point P,Q,S from origin is same.Means distance of point P from origin is same as distance of point S from origin i.e.
R is transitive.
Hence, R is an equivalence relation.
The set of all points related to a point are points whose distance from origin is same as distance of point P from origin.
In other words we can say there be a point O(0,0) as origin and distance between point O and point P be k=OP then set of all points related to P is at distance k from origin.
Hence, these set of points form circle with centre as origin and this circle passes through point P.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
The distance of point P from the origin is always the same as the distance of same point P from origin i.e.
Let
i.e. the distance of the point P from the origin is the same as the distance of the point Q from the origin.
this is the same as distance of the point Q from the origin is the same as the distance of the point P from the origin i.e.
Let
and
i.e. distance of the point P from the origin is same as the distance of the point Q from the origin, and also the distance of the point Q from the origin is same as the distance of the point S from the origin.
We can say that distance of point P, Q, S from the origin is the same. Means distance of point P from the origin is the same as the distance of point S from origin i.e.
Hence, R is an equivalence relation.
The set of all points related to a point
are points whose distance from the origin is the same as the distance of point P from the origin.
In other words, we can say there be a point O(0,0) as origin and distance between point O and point P be k=OP then set of all points related to P is at distance k from the origin.
Hence, these set of points form circle with the centre as the origin and this circle passes through point P.