Let the straight line y =2 x touch a circle with center (0, ), >0, and radius r at a point A _1. Let B _1 be the point on the circle such that the line segment A_1 B_1 is a diameter of the circle. Let +r=5+ 5 . Match each entry in List-I to the correct entry in List-II. The correct option is
C. ( P ) (4) ( Q ) (2) ( R ) (5) ( S ) (3)
Consider centre as P (0, ), >0 | 2(0)- 5 |=r aligned & |- |= 5 r \\& = 5 r \\& +r=5+ 5 \\& 5 r+r= 5 ( 5 +1) \\& r= 5 , =5 \\& P(0,5) aligned Foot of perpendicular from P to line 2 x - y =0 aligned & x-0 2 = y-5 -1 = -(2(0)-5) 5 =1 \\& x=2, y=4 A_1(2,4) aligned Let B ( p , q ) p +2 2 =0, q +4 2 =5 p =-2, q =6 ~B (-2,6)
Related: Mathematics — Circle · All PYQ Banks