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 the equation ax+by=1, cx ^2 +dy^2 =1 have only one solution then (a^2)/(c ) +(b^2)/(d)=

If the simultaneous linear equations a_(1)x+b_(1)y+c_(1)=0 " and " a_(2)x+b_(2)y+c_(2)=0 have only one solution, then the required condition is -

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

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)/(c)=(1)/(d)

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

Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if , 1/a-1/b=1/c-1/d

If 1,2,3 and 4 are the roots of the equation x^4 + ax^3 + bx^2 +cx +d=0 then a+ 2b +c=

If 1,2,3 and 4 are the roots of the equation x^4 + ax^3 + bx^2 +cx +d=0 then a+ 2b +c=