Let the straight line y = 2 x touch a circle with center ( 0 , α ) , α 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 o

Question

Let the straight line y = 2 x touch a circle with center ( 0 , α ) , α > 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 α + r = 5 + 5 ​ . Match each entry in List-I to the correct entry in List-II. The correct option is

TestHub · Accepted Answer

Consider centre as P ( 0 , α ) , α > 0 ​ 5 ​ 2 ( 0 ) − α ​ ​ = r ​ ∣ − α ∣ = 5 ​ r α = 5 ​ r ∴ α + r = 5 + 5 ​ 5 ​ r + r = 5 ​ ( 5 ​ + 1 ) r = 5 ​ , α = 5 ∴ P ( 0 , 5 ) ​ Foot of perpendicular from P to line 2 x − y = 0 ​ 2 x − 0 ​ = − 1 y − 5 ​ = 5 − ( 2 ( 0 ) − 5 ) ​ = 1 x = 2 , y = 4 A 1 ​ ( 2 , 4 ) ​ Let B ( p , q ) ∴ 2 p + 2 ​ = 0 , 2 q + 4 ​ = 5 ∴ p = − 2 , q = 6 B ( − 2 , 6 )

Mathematics - Circle Question with Solution | TestHub

Options:

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