" (1) "px^(2)+(2q-p^(2))x-2pq*p!=0

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the equation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is (i) p^(3)x^(2)+pq^(2)x+r=0 (ii) px^(2)-qx+r=0 (iii) p^(3)x^(2)-pq^(2)x+q^(2)r=0 (iv) px^(2)+qx-r=0

If p, q, r are rational then show that x^(2)-2px+p^(2)-q^(2)+2qr-r^(2)=0

Add : 6p^(2)q - 5pq^(2) -3pq, 8pq^(2)+2p^(2)q -2pq

Add : 6p^(2)q - 5pq^(2) -3pq, 8pq^(2)+2p^(2)q -2pq

If 25p^(2)+9q^(2)-r^(2)-30pq=0 a point on the line px+qy+r=0 is

A transversal cut the same branch of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 in P,P' and the anymptotes in Q.Q' ,the value of (PQ+PQ')-(P'Q'-P'Q)

A transvers axis cuts the same branch of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at P and P' and the asymptotes at Q and Q'. Prove that PQ=P'Q' and PQ'=P'Q.