If the equations `ax + by = 1` and `cx^2 +dy^2=1` have only one solution, prove that `a^2/c+ b^2/d = 1` and `x=a/c`,`y=b/d`

If a,b,c, a_1,b_1,c_1 are rational and equations ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have one and only one root in common, prove that b^2-ac and b_1^2-a_1c_1 must be perfect squares.

If x^2/a +y^2/b=1 and x^2/c+y^2/d=1 are orthogonal then relation between a , b , c , d is

If the equation ax^(2)+2bx+c=0 and ax62+2cx+b=0b!=c have a common root,then (a)/(b+c)=

If c^(2)=4d and the two equations x^(2)-ax+b=0 and x^(2)-cx+d=0 have one common root. then the value of 2(b+d) ) is equal to (A)? 13 ) ac (C) 2ac(D) ane

If a,b,c,d are in GP then prove that ax^3+bx^2+cx+d has a factor ax^2+c .

Ifc^(2)=4d and the two equations x^(2)-ax+b=0 and x^(2)-cx+d=0 have a common root,then the value of 2(b+d) is equal to 0 ,have one

if the lines ax+by+1=0cx+dy+1=0ex+fy+1=0 are concurrent then prove that (a,b),(c,d),(e,f) are collinear

If the curves ax^(2)+by^(2)=1 and cx^(2)+dy^(2)=1 intersect at right angles then show that (1)/(a)-(1)/(b)=(1)/(d)-(1)/(d)

If a,b,c and d are in G.P , then show that ax^(2)+c divides ax^(3)+bx^(2)+cx+d

If the quadratic equations,ax^(2)+2cx+b=0 and ax^(2)+2bx+c=0quad (b!=c) have a common root,then a+4b+4c is equal to: a.-2 b.-2 c.0 d.1