An ellipse with focii (1,4) and (α, β) touches x-axis at (5,0). Then value of (α-β) is

Question

An ellipse with focii (1,4) and (α, β) touches x-axis at (5,0). Then value of (α-β) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(1,4),(5,0) and reflection of (α, β) on x-axis are collinear |1 4 1 5 0 1 α -β 1|=0 ⇒ α-β=5

Q. An ellipse with focii $(1, 4)$ and $(α, β)$ touches $x$ -axis at $(5, 0)$ . Then value of $(α - β)$ is