Through any point P of the hyperbola a line QPR is drawn with a fixed gradient m, meeting the aymptotes in Q and R. Show that the products (QP).(PR)=`(a^2b^2(1+m^2))/(b^2-a^2m^2)`

The ordinate of any point P on the hyperbola, given by 25x^(2)-16y^(2)=400 ,is produced to cut its asymptotes in the points Q and R. Prove that QP.PR=25.

The ordinate of any point P on the hyperbola 25x^(2)-16y^(2)=400 is produced to cut the asymptoles in the points Q and R. Find the value of QP. PR

Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

Consider a curve ax^(2)+2hxy+by^(2)=1 and a point P not on the curve.A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (A) a parabola (D) an ellipse or hyperbola

PQR is a triangle right-angled at P and M is a point on QR such that P M_|_Q R . Show that P M^2=Q M.M R .

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 bx-ay=0 and bx+ay=0 at points Q and R, respectively. Then prove that CQ.CR=a^(2)+b^(2).

Comprehension (Q.6 to 8) A line is drawn through the point P(-1,2) meets the hyperbola x y=c^2 at the points A and B (Points A and B lie on the same side of P) and Q is a point on the lien segment AB. If the point Q is choosen such that PQ, PQ and PB are inAP, then locus of point Q is x+y(1+2x) (b) x=y(1+x) 2x=y(1+2x) (d) 2x=y(1+x)