Ques. 1JEE Advanced 2024 (Paper-1)
Let the straight line y=2x touch a circle with center (0, ), >0, and radius r at a point A1. Let B1 be the point on the circle such that the line segment A1B1 is a diameter of the circle. Let +r=5+ 5. Match each entry in List-I to the correct entry in List-II.
- (P) → (4) (Q) → (2) (R) → (1) (S) → (3)
- (P) → (2) (Q) → (4) (R) → (1) (S) → (3)
- (P) → (4) (Q) → (2) (R) → (5) (S) → (3)
- (P) → (2) (Q) → (4) (R) → (3) (S) → (5)
Answer
(3) (P) → (4) (Q) → (2) (R) → (5) (S) → (3)
Solution
Tangency: r= |2 0- | 5 = 5 r
r( 5+1)=5+ 5= 5( 5+1) r= 5, =5
A1 = foot of perpendicular from (0,5) on 2x-y=0: x-02= y-5-1=- (0-5)5=1 A1=(2,4)
B1=2(0,5)-(2,4)=(-2,6)
P → 4, Q → 2, R → 5, S → 3
Answer: (C)