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

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))

Find the tangent of the angle between the lines whose intercepts on the axes are respectively, p,-q and q, -p.

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

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

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that locus of the O centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2)) .

A variable plane which is at a constant 6 p from the origin meets the axes in A,B and C respectively. Show that the locus of the centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(4p^(2))

Let P(x_1,y_1) be a point and let ax + by +c =0 be a line. If L (h, k) is the foot of perpendicular drawn from P on this line and Q (alpha, beta) is the image of P in the given line, then prove that : (h-x_1)/a=(k-y_1)/b=-((ax_1+by_1+c)/(a^2+b^2)) .