[" The normal at a variable point "P" on an ellipse "(x^(2))/(a^(2))+(y^(2))/(b^(2))=1" of eccentricity e meets the axes of "],[" ellipse in "Q" and "R" then the locus of the mid-point of "QR" is a conic with an eccentricity e suchth "],[" (A) "e'" is independent of "e]

The normal at a variable point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 of eccentricity e meets the axes of the ellipse at Q and R .Then the locus of the midpoint of QR is a conic with eccentricity e' such that e' is independent of e(b)e'=1e'=e(d)e'=(1)/(e)

The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity e meets the axes of the ellipse at Qa n dRdot Then the locus of the midpoint of Q R is a conic with eccentricity e ' such that (a) e^(prime) is independent of e (b) e^(prime)=1 (c) e^(prime)=e (d) e^(prime)=1/e

The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity e meets the axes of the ellipse at Qa n dRdot Then the locus of the midpoint of Q R is a conic with eccentricity e ' such that (a) e^(prime) is independent of e (b) e^(prime)=1 (c) e^(prime)=e (d) e^(prime)=1/e

The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity e meets the axes of the ellipse at Qa n dRdot Then the locus of the midpoint of Q R is a conic with eccentricity e ' such that e^(prime) is independent of e (b) e^(prime)=1 e^(prime)=e (d) e^(prime)=1/e

Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentricity e is

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

The normal at a point P on the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2) of eccentricity e, intersects the coordinates axes at Q and R respectively. Prove that the locus of the mid-point of QR is a hyperbola of eccentricity (e )/(sqrt(e^(2)-1)) .