Let any double ordinate PNP' of the hyperbola `(x^(2))/(25)-(y^(2))/(16)=1` be produced on both sides to meet the asymptotes in Q and Q'. Then PQ.P'Q is equal to

Let any double ordinate P N P ' of the hyperbola (x^2)/(25)-(y^2)/(16)=1 be produced on both sides to meet the asymptotes in Qa n dQ ' . Then P QdotP^(prime)Q is equal to 25 (b) 16 (c) 41 (d) none of these

Let PQ be a double ordinate of the hyperboal (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 .If O be the centre of the hyperbola and OPQ is an equilateral triangle, then prove that the eccentricity e gt 2/sqrt(3) .

PQ is any double ordinate of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 , find the euqation to the locus of the point of trisection of PQ that is nearer to P .

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

Let P b any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose ordinate is PN. AA′ is its transverse axis. If the point Q divides AP in the ratio a^(2):b^(2) , then NQ is?

The line y = x intersects the hyperbola (x^(2))/(9) -(y^(2))/(25) = 1 at the points P and Q . The eccentricity of ellipse with PQ as major axis and minor axis of length (5)/(sqrt(2)) is _

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot

PQ is the double ordinate of the hyperbola x^2/a^2-y^2/b^2=1 and O is the centre of the hyperbola. If triangle OPQ is an equilateral triangle, then show that the eccentricity of this hyperbola is e) e^2 >4/3

Let P be a point on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and the line through P parallel to the y-axis meets the circle x^(2)+y^(2)=9 at Q, where P,Q are on the same side of the x-axis. If R is a point on PQ such that (PR)/(RQ)=(1)/(2) , then the locus of R is

From any point P lying in the first quadrant on the ellipse (x^2)/(25)+(y^2)/(16)=1,P N is drawn perpendicular to the major axis and produced at Q so that N Q equals to P S , where S is a focus. Then the locus of Q is (a) 5y-3x-25=0 (b) 3x+5y+25=0 (c) 3x-5y-25=0 (d) none of these