9. `x=asectheta , y=btantheta`

If x and y are connected parametrically by the equations given, without eliminating the parameter, Find (dy)/(dx) . x=asectheta, y=btantheta

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

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

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

Find the equations of the tangent and the normal to the curve (x^2)/(a^2)-(y^2)/(b^2)=1 at (asectheta,\ btantheta) at the indicated points.

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

If the normal at P(asectheta,btantheta) to the hyperbola x^2/a^2-y^2/b^2=1 meets the transverse axis in G then minimum length of PG is

If (asectheta, btantheta) and (asecphi, btanphi) be two coordinate of the ends of a focal chord passing through (ae,0) of x^2/a^2-y^2/b^2=1 then tan(theta/2)tan(phi/2) equals to

Find the equation of circle whose : (i) radius is 5 and centre is (3,4). (ii) radius is sqrt(5) and centre is (0.2). (iii) radius is sqrt(a^(2)+b^(2)) and centre is (a,b). (iv) radius is r and centre is (rcostheta,rsintheta) . (v) radius is sqrt(a^(2)sec^(2)theta+b^(2)tan^(2)theta) and centre is (asectheta,btantheta) .