The equation `a^2x^2+2h(a+b)x y+b^2y^2=0` and `a x^2+2h x y+b y^2=0` represent

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a x^2-2h x y-b y^2=0 b x^2-2h x y+a y^2=0 b x^2+2h x y+a y^2=0 a x^2-2h x y+b y^2=0

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a x^2-2h x y-b y^2=0 b x^2-2h x y+a y^2=0 b x^2+2h x y+a y^2=0 a x^2-2h x y+b y^2=0

The equation (x^2 - a^2)^2 + (y^2 - b^2)^2 = 0 represents points

The equation y^(2)-x^(2)+2x-1=0 , represents

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

The equation of the parabola whose vertex is (a ,0) and the directrix has the equation x+y=3a is a. x^2+y^2+2x y+6a x+10 a y+7a^2=0 b. x^2-2x y+y^2-6a x+10 a y+7a^2=0 c. x^2-2x y+y^2+6a x+10 a y+7a^2=0 d.None of these

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A) (a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B) (a+b)(x^2+y^2)=2a b (C) (x^2+y^2)=(a^2+b^2) (D) (a-b)^2(x^2+y^2)=a^2b^2

If the conics whose equations are S-=sin^2thetax^2+2h x y+cos^2thetay^2+32 x+16 y+19=0,S^(prime)-=cos^2thetax^2+2h^(prime)x y+s in^2thetay^2+16 x+32y+19=0 intersect at four concyclic points, then, (where theta in R) h+h^(prime)=0 (b) h=h ' h+h^(prime)=1 (d) none of these