Question

The straight line x+2y = 1 meets the
coordinate axes at A and B. A circle is
drawn through A,B and the origin. Then
the sum of perpendicular distances from
A and B on the tangent to the circle at the
origin is
​

Answer 1

let us take out the point A and B

when ,the line intersect at y axis then it's abcissa will be zero...

put this in the given eqaution....

0-2y=1

Y=-1/2

hence coordinates of A is(0,-1/2)

no,when the same line interecft at y-axis then it's ordinate will be zero

put this in eqaution of line

x=1

hence coordinates of B is (1,0)

eqaution of circle will be

(x-1)(x-0))+(y-0)(y-1/2)=0

x^2+y^2-x-y/2=0

now,we know, eqaution of tangent,as x+2y=1

also

then sum=2/√5 +1/2√5

=(4+1)/2√5

=5/2√5

=√5/2

hope it helps you