Line `L` has intercepts `a and b` on the coordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line `L` has intercepts `p and q`. Then (a) `a^2+b^2=p^2+q^2` (b) `1/(a^2)+1/(b^2)=1/(p^2)+1/(q^2)` (c) `a^2+p^2=b^2+q^2` (d) `1/(a^2)+1/(p^2)=1/(b^2)+1/(q^2)`

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through given angle, keeping the origin fixed, the same line L has intercepts p and q, 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) .

The intercepts of a straight line upon the coordinate axes are a and b . If the length of the perpendicular on this line from the origin be p, prove that (1)/(a^(2))+(1)/(b^(2))=(1)/(p^(2)) .

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is (A) (x^2+y^2)(1/(x^2)+1/(y^2))=4a^2 (B) (x^2+y^2)^2(1/(x^2)+1/(y^2))=a^2 (C) (x^2+y^2)^2(1/(x^2)+1/(y^2))=4a^2 (D) (x^2+y^2)(1/(x^2)+1/(y^2))=a^2

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2

A straight line passes through P (1,2) and is such that its intercept between the axes is bisected at P. Then the equation of the line is-

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

The points A and B trisect the line -segment joining the points P(2,1-3) and Q(5,-8,3) , find the coordinates of the points A and B.

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)

Let P(a sectheta, btantheta) and Q(asecphi , btanphi) (where theta+phi=pi/2 ) be two points on the hyperbola x^2/a^2-y^2/b^2=1 If (h, k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^2+b^2)/a (B) -((a^2+b^2)/a) (C) (a^2+b^2)/b (D) -((a^2+b^2)/b)