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^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 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 prove that a-b/h = a'-b'/h'

Two conics a_1x^2+2h_1xy + b_1y^2 = c_1, a_2x^2 + 2h_2xy+b_2y^2 = c_2 intersect in 4 concyclic points. Then

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

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2.

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

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