Question

prove that chord of contact of a pair of tangents to the circle x^2+y^2=1 drawn from any point on the line 2x+y=4 passes through a fixed point. Also, find the coordinates of that points​

Answer 1

Answer:

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Step-by-step explanation:

Let (a,b) be a point on 2x+y=4

Then

2a+b=4…..(1)

The chord of contact of a pair of tangents from (a,b) is

ax+by=1……(2)

Divide (1) by 4 and subtract it from (2)

a(x−12)+b(y−14)=0

This shows that (

2

1

,

4

1

)always lie on the chord of contact for any value of a and b.