AP EAMCET201920 Apr 2019Evening ShiftMathematicsStraight LinesActual
A line passing through P(4,2) cuts the coordinate axes at A and B respectively. If O is the origin, then the locus of the centre of the circum-circle of O A B is
Options
- Ax⁻¹+y⁻¹=2
- B2 x⁻¹+y⁻¹=1
- Cx⁻¹+2 y⁻¹=1
- D2 x⁻¹+3 y⁻¹=1
Correct answer
B. 2 x⁻¹+y⁻¹=1
Step-by-step solution
Let a line cuts the coordinate axes at A and B respectively is Now, coordinate of centre of the circumcircle of O A B is mid-point of hypotenuse of right angle O A B and it is mid-point of A B . So, centre of the circumcircle of O A B is ( a 2 , b 2 ) . Now, from Eq. (ii), on taking locus of point ( a 2 , b 2 ) , we get aligned 2 x + 1 y & =1 2 x⁻¹+y⁻¹ & =1 aligned Hence, option (b) is correct.