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

If (asectheta;btantheta) and (asecphi; btanphi) are the ends of the focal chord of x^2/a^2-y^2/b^2=1 then prove that tan(x/a)tan(phi/2)=(1-e)/(1+e)

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^2 - y^2/b^2 = 1 passes through a focus, prove that tan (theta/2) tan (phi/2) + (e-1)/(e+1) = 0 .

If theta and phi are eccentric angles of the ends of a pair of conjugate diametres of the ellipse x^2/a^2 + y^2/b^2 = 1 , then (theta - phi) is equal to

Let P(a sectheta, btantheta) and Q(asecphi , btanphi) (where theta+phi=pi/2 ) be two points on the hyperbola x^2/a^2-y^2/b^2=1 If (h, k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^2+b^2)/a (B) -((a^2+b^2)/a) (C) (a^2+b^2)/b (D) -((a^2+b^2)/b)

Let P(a sectheta, btantheta) and Q(aseccphi , btanphi) (where theta+phi=pi/2 be two points on the hyperbola x^2/a^2-y^2/b^2=1 If (h, k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^2+b^2)/a (B) -((a^2+b^2)/a) (C) (a^2+b^2)/b (D) -((a^2+b^2)/b)

If the chord joining the points (a sectheta_1, b tantheta_1) and (a sectheta_2, b tantheta_2) on the hyperbola x^2/a^2-y^2/b^2=1 is a focal chord, then prove that tan(theta_1/2)tan(theta_2/2)+(ke-1)/(ke+1)=0 , where k=+-1

The least length of chord passing through (2,1) of the circle x^(2)+y^(2)-2x-4y-13=0 is

If 2sec 2theta=tan phi+cotphi , then one of the values of theta+phi is

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

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .