The is a point P on the hyperbola `(x^(2))/(16)-(y^(2))/(6)=1` such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is

The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is (a) -64/5 (b) -32/9 (c) -64/9 (d)none of these

There is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(9)=116169 such that its distance to the right directrix is the average of its distance to the two foci.Let the x-coordinate of P be (m)/(n) with m and n being integers,(n>0) having no common factor except 1.Then n-m equals

A point P on the ellipse (x^(2))/(2)+(y^(2))/(1)=1 is at distance of sqrt(2) from its focus s. the ratio of its distance from the directrics of the ellipse is

A point P lies on the ellipe ((y-1)^(2))/(64)+((x+2)^(2))/(49)=1 . If the distance of P from one focus is 10 units, then find its distance from other focus.

A point P lies on the ellipe ((y-1)^(2))/(64)+((x+2)^(2))/(49)=1 . If the distance of P from one focus is 10 units, then find its distance from other focus.

A point P lies on the ellipe ((y-1)^(2))/(64)+((x+2)^(2))/(49)=1 . If the distance of P from one focus is 10 units, then find its distance from other focus.

Let P be a point on the ellipse (x^(2))/(16) + (y^(2))/(9) = 1 . If the distance of P from centre of the ellipse be equal with the average value of semi major axis and semi minor axis, then the coordinates of P is _

A series of hyperbola are drawn having a common transverse axis of length 2a. Prove that the locus of point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptote, is the curve (x^2-y^2)^2 =lambda x^2 (x^2-a^2), then lambda equals