wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let T be the line passing through the points P(2,7) and Q(2,5). Let F1 be the set of all pairs of circles (S1,S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say, M. Let E1 be the set representing the locus of M as the pair (S1,S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1,1) be F2. Let E2 be the set of the mid-points of the line segments in the set F2. Then, which of the following statement(s) is (are) TRUE?

A
The point (2,7) lies in E1.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
The point (45,75) does NOT lie in E2.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
The point (12,1) lies in E2.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
The point (0,32) does NOT lie in E1.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
B The point (45,75) does NOT lie in E2.
D The point (0,32) does NOT lie in E1.

PL=ML [O1PLO1ML]
and ML=QL [O2MLO2QL]
PL=QL=ML
L is the mid-point of PQ.
Thus, coordinates of L is (0,1).
Let coordinates of M be (x,y).
ML=PL(x0)2+(y1)2=40
Therefore, locus of M is a circle with centre (0,1) and radius 40.
E1={(x,y):(x0)2+(y1)2=40}
Clearly, (2,7) does not lie in E1.
Also, (0,32) does not lie in E1.


Locus of points in E2 is a circle with coordinates of diameter L(0,1) and R(1,1).
E2={(x,y):(x0)(x1)+(y1)(y1)=0}
i.e, E2={(x,y):x(x1)+(y1)2=0}
(45,75),(12,1) does not lie in E2.

flag
Suggest Corrections
thumbs-up
40
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circle and Point on the Plane
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon