The straight line x+2 y=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:

Step-by-step solution

Let equation of circle be x²+y²+2 g x+2 f y=0 As length of intercept on x axis is 1=2 g²-c |g|= 1 2 length of intercept on y -axis = 1 2 =2 f²-c |f|= 1 4 Equation of circle that passes through given points is x²+y²-x- y 2 =0 Tangent at (0,0) is, (y-0)= ( d y d x )_ (0,0) ^ (x-0) ( x -0) 2 x+y=0 Perpendicular distance from B(1,0) on the tangent to the circle = 1 2 5 Perpendicular distance from B (0, 1 2 ) on the tangent to the circle = 2 5 Sum of perpendicular distance = 1 2 +2 5 = 5 2 .