If the length of the perpendicular from the point `(1, 1)` to the line `ax-by+c=0` be , show that `1/c + 1/a - 1/b = c/(2ab)`

If the length of the perpendicular from the point (1,1) to the line ax-by+c=0 be unity,show that (1)/(c)+(1)/(a)-(1)/(b)=(c)/(2ab)

(i ) If the length of perpendicular from origin to the line ax+by+a+b=0 is p , then show that : p^(2)-1=(2ab)/(a^(2)+b^(2)) (ii) If the length of perpendicular from point (1,1) to the line ax-by+c=0 is unity then show that : (1)/(a)-(1)/(b)+(1)/(C )=(c )/(2ab)

Foot of the perpendicular from a point (x_(1),y_(1)) on the line ax + by + c= 0 is given by

If the product of the perpendiculars drawn from the point (1,1) on the lines ax^(2)+2hxy+by^(2)=0 is 1, then

Find the length of perpendicular from the point A(1,4,-2) to the line joining (2,1,-2) and (0,-5,1)

If p is the length of perpendicular from point (1,1) to the straight line ax+by+a+b=0 , then prove that : p^(2)=4+(8ab)/(a^(2)+b^(2))

If theta is the acute angle between the lines with slopes m1 and m2 then tan theta=(m_(1)-m_(2))/(1+m_(1)m_(2)) 2) if p is the length the perpendicular from point P(x1,y1) to the line ax +by+c=0 then p=(ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))

Consider the following statements : 1. The length p of the perpendicular from the origin to the line ax+by=c satisfies the relation p^(2)=c^(2)/(a^(2)+b^(2)) The length p of the pependicular from the origin to the line x/a+y/b=1 satisfies the relation 1/p^(2)=1/a^(2)+1/b^(2) . 3. The length p of the perpendicular from the origin to the line y=mx+c satisfies the relation 1/p^(2)=(1+m^(2)+c^(2))/c^(2) Which of the above is/are correct ?

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b,then show that (1)/(p^(2))=(1)/(a^(2))+(1)/(b^(2))