if `P` is the length of perpendicular from origin to the line `x/a+y/b=1` then prove that `1/(a^2)+1/(b^2)=1/(p^2)`

If p is the length of perpendicular from the origin on the line (x)/(a) + (y)/( b) =1 and a^(2), p^(2) and b^(2) are in A.P., then show that a^(4) + b^(4) =0 .

Length of perpendicular from origin to the line (x)/(a) + (y)/( b) = 1 is p . If a^(2) , p^(2) and b^(2) are in A.P. then prove that a^(4) + b^(4) =0 .

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) .

P_1 and P_2 are the length of perpendicular from origin to the line x sec theta + y cosec theta =a and x cos theta - y sin theta = a cos 2 theta then ….... of the following is valid.

If p and q are the lengths of perpendiculars from the origin to the lines x cos theta - y sin theta = k cos 2 theta and x sec theta + y cosec theta=k respectively, prove that p^(2) + 4q^(2) = k^(2) .

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

Find the length of the perpendicular drawn from point (2,3,4) to line (4-x)/2=y/6=(1-z)/3dot

The length of the perpendicular drawn from the point (3, -1, 11) to the line (x)/(2)=(y-2)/(3)=(z-3)/(4) is

Find the length of perpendicular from P(2, -3, 1) to the (x+1)/(2)=(y-3)/(3)=(z+2)/(-1) .

The line (x)/(a) + (y)/( b) =1 moves in such a way that (1) /( a^2) + (1)/( b^2) = (1)/( c^2) , where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x^2 + y^2 = c^2