An infinite number of tangents can be drawn from (1, 2) to the circle x2 + y2 -2x - 4y + λ = 0 then λ=

Question

An infinite number of tangents can be drawn from (1, 2) to the circle x2 + y2 -2x - 4y + λ = 0 then λ= (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Clearly the point (1, 2) is the centre of the given circle and infinite tangents can only be drawn on a point circle. Hence the radius should be 0. ∴ √12 +22 -λ =0 ⇒ λ =5

Q. An infinite number of tangents can be drawn from $(1, 2)$ to the circle $x^{2} + y^{2} - 2 x - 4 y + λ = 0$ then $λ =$

Clearly the point $(1, 2)$ is the centre of the given circle and infinite tangents can only be drawn on a point circle. Hence the radius should be $0$ .
$∴ 1^{2} + 2^{2} - λ = 0 \Rightarrow λ = 5$

Q. An infinite number of tangents can be drawn from (1,2) to the circle x2+y2−2x−4y+λ=0 then λ=

Clearly the point (1,2) is the centre of the given circle and infinite tangents can only be drawn on a point circle. Hence the radius should be 0. ∴12+22−λ​=0⇒λ=5

Q. An infinite number of tangents can be drawn from $(1, 2)$ to the circle $x^{2} + y^{2} - 2 x - 4 y + λ = 0$ then $λ =$

Clearly the point $(1, 2)$ is the centre of the given circle and infinite tangents can only be drawn on a point circle. Hence the radius should be $0$ .
$∴ 1^{2} + 2^{2} - λ = 0 \Rightarrow λ = 5$