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

If p be the length of the perpendicular from the origin on the line x/a+y/b=1 , then

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 .

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

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)) .

If P is the length of perpendicluar drawn from the origin to any normal to the ellipse x^(2)/25+y^(2)/16=1 , then the maximum value of p is

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

Let d be the perpendicular distance from the centre of the ellipse x^2/a^2+y^2/b^2=1 to the tangent drawn at a point P on the ellipse. If F_1 & F_2 are the two foci of the ellipse, then show the (PF_1-PF_2)^2=4a^2(1-b^2/d^2) .

A point P(x,y) nores on the curve x^(2/3) + y^(2/3) = a^(2/3),a >0 for each position (x, y) of p, perpendiculars are drawn from origin upon the tangent and normal at P, the length (absolute valve) of them being p_1(x) and P_2(x) brespectively, then

If p_(1),p_(2),p_(3) be the length of perpendiculars from the points (m^(2),2m),(mm',m+m') and (m^('2),2m') respectively on the line xcosalpha+ysinalpha+(sin^(2)alpha)/(cosalpha)=0 then p_(1),p_(2),p_(3) are in:

If p_1, p_2, p_3 are the altitudes of a triangle from the vertices A, B, C and triangle , the area of the triangle, prove that : p_1^-2 + p_2^-2 + p_3^-2 = ((cot A+cot B+ cotC))/triangle .