Question

if p is perpendicular from the origin to the line ax+by+c=0then prove provethat p = in bracket c upon under root a square+b square bracket complete​

Answer 1

bhi178 The Sage

concept : use intercept form of line : x/a + y/b = 1 and then find perpendicular distance of point from line .

equation of line in intercept form is

x/a + y/b = 1

x/a + y/b - 1 = 0 .

now, use formula

distance of point (x1, y1) from line : ax + by + c =0 is |ax1 + by1 + c|/√(a²+b²)

so, it's distance from origin is

P = | 0 + 0 -1|/√(1/a² + 1/b²)

P = 1/√(1/a² + 1/b²)

1/P = √(1/a² + 1/b²)

take square both sides,

1/P² = 1/a² + 1/b²

hence proved.