If `x=asectheta` and `y=btantheta` , then `b^2x^2-a^2y^2=`
(a)`a b`
(b) `a^2-b^2`
(c) `a^2+b^2`
(d) `a^2b^2`

If x=acostheta and y=bsintheta , then b^2x^2+a^2y^2= (a) a^2b^2 (b) a b (c) a^4\ b^4 (d) a^2+b^2

If x=asintheta and y=btantheta, then prove that (a^2)/(x^2)-(b^2)/(y^2)=1

If x=asectheta,y=btantheta,"prove that"(d^2y)/(dx^2)=-(b^4)/(a^2y^3)

If x=asectheta , y=btantheta , prove that (d^2y)/(dx^2)=-(b^4)/(a^2\ y^3) .

If x=asectheta+btantheta and y=atantheta+bsectheta ,prove that : x^2-y^2=a^2-b^2 .

x+y=a+b , a x-b y=a^2-b^2

Area of the quadrilateral formed with the foci of the hyperbola x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1 (a) 4(a^2+b^2) (b) 2(a^2+b^2) (c) (a^2+b^2) (d) 1/2(a^2+b^2)

If (a , b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x , then (a) a=2b (b) a^2=2b (c) a^2=2b (d) 2a=b^2

If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0 has perpendicular diagonals, then (a) b^2+c^2=b^('2)+c^('2) (b) c^2+a^2=c^('2)+a^('2) (c) a^2+b^2=a^('2)+b^('2) (d) none of these

The product of the perpendicular from two foci on any tangent to the hyperbola x^2/a^2-y^2/b^2=1 is (A) a^2 (B) (b/a)^2 (C) (a/b)^2 (D) b^2