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Tangents are drawn from the points on th...

Tangents are drawn from the points on the line x-y-5=0 to `x^(2)+4y^(2)=4` . Prove that all the chords of contact pass through a fixed point

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Variable point on the line x-y-=5 can be taken as (t,t-5) t `in R`.
Chord of contact of the ellipse `x^(2)+4y^(2)=4 ` w.r.t. this point is
`tx+4(t-5)y-4=0`
or `(-20y-4)+t(x+4y)`
This is the equation of family of straigth lines,
Each member of this family passes through the point of intersection of straigth lines `-20y-4=0 and x+y0` which is `((1)/(5),-(4)/(5))`
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