The equation `sin^2theta=(x^2+y^2)/(2x y),x , y!=0` is possible if

Show that the equation sec^2 theta=(4xy)/(x+y)^2 is only possible when x=y

Prove that sin^2theta=(x+y)^2/(4xy) is possible for real values of x and y only when x = y , y!=0 and x!=0 .

If sin^(2)theta=(x^(2)+y^(2)+1)/(2x) . Find the value of x and y.

A curve satisfies the differential equation (dy)/(dx)=(x+1-xy^2)/(x^2y-y) and passes through (0,0) (1) The equation of the curve is x^2+y^2+2x=x^2y^2 (2) The equation of the curve is x^2+y^2+2x+2y=x^2y^2 (3) x=0 is a tangent to curve (4) y=0 is a tangent to curve

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

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

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

Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2 hold simultaneously. the possible value of a is ___________

Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2 hold simultaneously. the possible value of a is ___________

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