A line making equal intercepts on coordinate axes and is tangent to the circle x^2 + y^2 = 4 . The length of each intercept made by line on the coordinate axes is ...

Step-by-step solution

Let the equation of the line making equal intercepts on the coordinate axes be x a + y a = 1 . This can be written as x + y - a = 0 . The line is tangent to the circle x^2 + y^2 = 4 . The center of the circle is (0, 0) and its radius is 2 . For a line to be tangent to a circle, the perpendicular distance from the center of the circle to the line must be equal to the radius. |0 + 0 - a| 1^2 + 1^2 = 2 |a| 2 = 2 |a| = 2 2 The length of each intercept made by the line on the coordinate axes is 2 2 .