If p is 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 whose intercepts will the coordinate axes are (1)/(3) and (1)/(4) then the value of p is

If p_(1) " and " p_(2) are the lengths of the perpendiculars from the origin to the straight lines xsectheta+ycosectheta=2a " and " xcostheta-ysintheta=acos2theta , then prove that p_(1)""^(2)+p_(2)""^(2)=a^(2) .

If p_(2),p_(2),p_(3) are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))

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)) .

Find the equation of the line passing through (2,-1) and whose intercepts on the axes are equal in magnitude but opposite in sign.

P_(1) and P_(2) are the lengths of the perpendicular from the foci on the tangent of the ellipse and P_(3) and P_(4) are perpendiculars from extermities of major axis and P from the centre of the ellipse on the same tangent, then (P_(1)P_(2)-P^(2))/(P_(3)P_(4)-P^(2)) equals (where e is the eccentricity of the ellipse)

The line L has intercepts a and b on the coordinate axes. Keeping the origin fixed, the coordinate axes are rotated through a fixed angle. If the line L has intercepts p and q on the rotated axes, then (1)/(a^(2))+(1)/(b^(2))  is equal to

If a tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 makes intercepts h and k on the co-ordinate axes then show that a^(2)/h^(2)+b^(2)/k^(2)=1 .

The equation of a straight line through (2,1) with equal intercepts on the coordinate axes is :