" 10."quad c^(2)(x^(2)+y^(2))=x^(2)y^(2)quad " at "((c)/(cos theta),(c)/(sin theta))

A hyperbola having the transverse axis of length 2sin theta is confocal with the ellipse 3x^(2)+4y^(2)=12 .Then its equation is x^(2)csc^(2)theta-y^(2)sec^(2)theta=1x^(2)sec^(2)theta-y^(2)cos ec^(2)theta=1x^(2)sin^(2)theta-y^(2)cos^(2)theta=1x^(2)cos^(2)theta-y^(2)sin^(2)theta=1

If cos^(-1)x+cos^(-1)y=theta show that x^(2)-2xy cos theta+y^(2)=sin^(2)theta

If x=a cos theta and y=b sin theta, then b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2)( b) ab(c)a^(4)b^(4)(d)a^(2)+b^(2)

The parametric form of the ellipse 4 (x +1) ^(2) + (y-1) ^(2) = 4 is a) x = cos theta -1 , y =2 sin theta -1 b) x = 2 cos theta-1 , y =2 sin theta -1 c) x = cos theta - 1, y = 2 sin theta + 1 d) x = cos theta +1, y =2 sin theta +1

If sin theta=(x^2-y^2)/(x^2+y^2) then find the values of cos theta and cot theta

Radius of the circle x^(2)+y^(2)+2x cos theta+2y sin theta-8=0, is

If cos ^(-1) x+ cos ^(-1) y= theta , show that x^(2)-2xycos theta +y^(2)=sin ^(2) theta

int(cos2x-cos2 theta)/(cos x-cos theta)dx is equal to 2(sin x-cos theta)+C(b)2(sin x+x cos theta)+C(b)2(sin x-x cos theta)+C(d)2(sin x+2x cos theta)+C(d)2(sin x-2x cos theta)+C

If x = (sin^(3)theta)/(cos^(2) theta)and y = (cos^(3) theta)/(sin^(2)theta) , where sin theta + cos theta = (1)/(2) , " then " x + y =

Let 0 leq theta leq (pi)/(2) and x=X cos theta+Y sin theta y=X sin theta-Y cos theta such that x^(2)+4 x y+y^(2)=a X^(2)+b Y^(2) where a, b are constants, then