Most Important Selected Qs for JEE AdvancedMathematicsCircle
Consider two circles C₁: x^2+y^2-1=0 and C₂: x^2+y^2-2=0 . Let A(1,0) be a fixed point on the circle C₁ and B be any variable point on the circle C₂ . The line BA meets the curve C₂ again at C . Which of the following alternative(s) is/are correct?
Options
- AOA ^2+ OB ^2+ BC ^2 [7,11] , where O is the origin
- BOA ^2+ OB ^2+ BC ^2 [4,7] , where O is the origin.
- CLocus of midpoint of AB is a circle of radius 1 2
- DLocus of midpoint of A B is a circle of area 2
Correct answer
C. Locus of midpoint of AB is a circle of radius 1 2
Step-by-step solution
We have maximum BC =2 2 and minimum BC =2 OA ^2+ OB ^2+ BC ^2 [7,11] Let M be the midpoint of A B . M ( 1+ 2 2 , 2 2 )=(h, k) = 2 k 2 , = 2 ~h -1 2 Now on squaring & adding, we get 4 k ^2+(2 ~h -1)^2=2 Locus of M(h, k) is (x- 1 2 )^2+y^2= ( 1 2 )^2