If C is the centre of a hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , S, S its foci and P a point on it. Prove tha SP. S'P `=CP^2-a^2+b^2`

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

Let 'p' be the perpendicular distance from the centre C of the hyperbola x^2/a^2-y^2/b^2=1 to the tangent drawn at a point R on the hyperbola. If S & S' are the two foci of the hyperbola, then show that (RS + RS')^2 = 4 a^2(1+b^2/p^2) .

if S and S are two foci of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ( altb ) and P(x_(1) , y_(1)) a point on it then SP+ S'P is equal to

If any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C, meets its director circle in P and Q, show that CP and CQ are conjugate semi-diameters of the hyperbola.

A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having its foci as S_1 and S_2 . If the internal angle bisector of the angle angleS_1PS_2 cuts the x-axis at poin Q(alpha, 0) then range of alpha is

If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci S a n d S ' and eccentricity e , then prove that the area of Δ S P S ' is be sqrt(a^2-alpha^2)

If S and T are foci of x^(2)/(16)-y^(2)/(9)=1 . If P is a point on the hyperbola then |SP-PT|=

If P is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 , S and S ’ are the foci of the ellipse then find SP + S^1P

P is any point on the ellipise (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and S and S' are its foci, then maximum value of the angle SPS' is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is