The Total solution for NCERT class 6-12
If p is the length ofperpendicular from the origin to the line whose intercepts on the axes are aand b, then show that 1/p2 = 1/a2 + 1/b2
Equation of a line whose intercepts on the axes are a and bis x/a + y/b = 1
bx + ay = ab
bx + ay – ab = 0 ………………..(1)
Perpendicular distance (d) of a line Ax + By + C = 0 from apoint (x1, y1) is given by
Now square on both the sides we get
∴ 1/p2 = 1/a2 + 1/b2
Hence proved.