Prove that the length of perpendicular from a point `(x_1,y_1)` to a line `ax+by+c=0` is `|(ax_1+by_1+c)/(sqrt(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)))

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

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)

Fill in the blanks (c) The length of perpendicular from a point (1, 2) to a line 3x + 4y + 5 = 0 is _________.

(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)

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)

Prove that the product of the length of the perpendiculars from the points (sqrt(a^2 -b^2) , 0) and (-sqrt(a^2 -b^2), 0) to the line x/a cos theta + y/a cos theta + y/b sin theta = 1 is

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 Q(h,k) is the foot of the perpendicular from P(x_(1) ,y_(1)) on the line ax + by+ c=0 then Q(h,k) is