a straight line through A (2,1) is such that its intercept between the axis is bisected at A. its equation is

Dear Student,

Follow the given steps –

Let the line through A meets the x – axis and y – axis on B(a,0) and C(0,b) respectively.
Since A is the mid point of B and C, thus we can make the equation as
(a-2)² + 1² = 2² + (b-1)² ----- (1)
Next, equation through B and C will be,
y = (b/a)x + b or ay = bx + ab. ----- (2)
Since (2) passes through A thus,
a = b(2+a) ---- (3)
Using (1) and (3) find the values of a and b and put them in (2) to get the answers.

Thanks.