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

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+sin^2thetay^2+16 x+32y+19=0 intersect at four concyclic points, then, (where theta in R) (a) h+h^(prime)=0 (b) h=h ' (c) h+h^(prime)=1 (d) none of these

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

If the conics whose equations are S_1:(sin^2theta)x^2+(2htantheta)x y+(cos^2theta)y^2+32 x+16 y+19=0 S_2:(cos^2theta)x^2-(2h^(prime)cottheta)x y+(sin^2theta)y^2+16 x+32 y+19=0 intersect at four concyclic points, where theta[0,pi/2], then the correct statement(s) can be (a) h+h^(prime)=0 (b) h-h^(prime)=0 (c) theta=pi/4 (d) none of these

If the conics whose equations are S_1:(sin^2theta)x^2+(2htantheta)x y+(cos^2theta)y^2+32 x+16 y+19=0 S_2:(cos^2theta)x^2-(2h^(prime)cottheta)x y+(sin^2theta)y^2+16 x+32 y+19=0 intersect at four concyclic points, where theta[0,pi/2], then the correct statement(s) can be (a) h+h^(prime)=0 (b) h-h^(prime)=0 (c) theta=pi/4 (d) none of these

If the conics whose equations are S_1:(sin^2theta)x^2+(2htantheta)x y+(cos^2theta)y^2+32 x+16 y+19=0 S_1:(sin^2theta)x^2-(2h^(prime)cottheta)x y+(sin^2theta)y^2+16 x+32 y+19=0 intersect at four concyclic points, where theta[0,pi/2], then the correct statement(s) can be h+h^(prime)=0 (b) h-h^(prime)=0 theta=pi/4 (d) none of these

If the conics whose equations are S_(1):(sin^(2)theta)x^(2)+(2h tan theta)xy+(cos^(2)theta)y^(2)+32x+16y+19=0S_(1):(sin^(2)theta)x^(2)-(2h'cot theta)xy+(sin^(2)theta)y^(2)+16x+32y+19=0 intersect at four concyclic points,where theta epsilon[0,(pi)/(2)], then the correct statement(s) can be h+h'=0 (b) h-h'=0 theta=(pi)/(4)(d) none of these

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 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 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

If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2y^2+2a x+2b y+c=0 intersect othrogonally, then prove that a a^(prime) + b b prime=c+c^(prime)/2dot