Tangents are drawn from points on the line $x - y + 2 = 0$ to the ellipse $x^{2} + 2 y^{2} = 2$ , then all the chords of contact pass through the point whose distance from $(2, \frac{1}{2})$ is

Question

Tangents are drawn from points on the line x − y + 2 = 0 to the ellipse x 2 + 2 y 2 = 2 , then all the chords of contact pass through the point whose distance from ( 2 , 2 1 ​ ) is

TestHub · Accepted Answer

Consider any point ( t 1 ​ , t + 2 ) , t ∈ R on the line x − y + 2 = 0 The chord of contact of ellipse with respect to this point is x ( t ) + 2 y ( t + 2 ) − 2 = 0 ⇒ ( 4 y − 2 ) + t ( x + 2 y ) = 0 , y = 2 1 ​ , x = − 1 Hence, the point is ( − 1 , 2 1 ​ ) , Where distance from ( 2 , 2 1 ​ ) is 3 .

Mathematics - Ellipse Question with Solution | TestHub

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