Let `F_1 and F_2` be the points (2,-1) and (-1,3) respectively. Does there exists any point P such that `|F_1P| + |F_2P| = 3`?

Let C_1 and C_2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let P be any point on C_1 and Q be any point C_2 . Let P_1 and Q_1 be the reflection of P and Q, respectively w.r.t the line y = x then prove that P_1 lies on C_2 and Q_1 lies on C_1 and PQ >= [P P_1, Q Q_1] . Hence or otherwise , determine points P_0 and Q_0 on the parabolas C_1 and C_2 respectively such that P_0 Q_0 <= PQ for all pairs of points (P,Q) with P on C_1 and Q on C_2

Find p if the points (p+1,1), (2p + 1,3) and (2p + 2, 2p) are collinear.

If E and F are the complementary events of events E and F , respectively, and if P(F) in [0,1]

Let f:R rarr R defined by f(x) = x^2 + 1 , then pre image of 17 and -3 respectively are

If f_(1) ,(x) and f_(2)(x) are defined on a domain D_(1) , and D_(2) , respectively, then domain of f_(1)(x) + f_(2) (x) is :

Let F1,F_2 be two focii of the ellipse and PT and PN be the tangent and the normal respectively to the ellipse at ponit P.then

A circle has the same center as an ellipse and passes through the foci F_1a n dF_2 of the ellipse, such that the two curves intersect at four points. Let P be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of triangle P F_1F_2 is 30, then the distance between the foci is

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. Let T_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m_1^ 2)+m_2^ 2) is

Let f : R rarr R be defined by f(x) =x^2 +1 . Then preimages of 17 and -3 respectively, are