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_(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

If two curves whose equations are ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 and a'x^(2)+2h'xy+b'y^(2)+2g'x+2f'y+c=0 intersect in four concyclic point.then

Two conics a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=c_(1),a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=c_(2) intersect in 4 concyclic points.Then

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

The equations a^2x^2+2h(a+b)xy+b^2y^2=0 and ax^2+2hxy+by^2=0 represent.

If a cos theta+bs int h eta=x and a sin theta-b cos theta=y, prove that a^(2)+b^(2)=x^(2)+y^(2)

The square of the intercept made by the circle x^(2)+y^(2)+2hx cos theta+2ky sin theta-h^(2)sin^(2)theta=0 on the x- axis is

If cos(x-y), cosx and cos(x+y) are in H.P., then cos x sec (y/2) equals