An ellipse E has its centre C(1,3) focus at S(6,3) and passing through the point P(4,7) then If the normal at a variable point on the ellipse (E) meets its axes in Q and R then the locus of the mid point of Q R is a conic with an eccentricity ( e prime), then -

Question

An ellipse E has its centre C(1,3) focus at S(6,3) and passing through the point P(4,7) then If the normal at a variable point on the ellipse (E) meets its axes in Q and R then the locus of the mid point of Q R is a conic with an eccentricity ( e prime), then - (A) e prime=(3/√10) (B) e prime=(√5/3) (C) e prime=(3/√5) (D) e prime=(√10/3)

Tardigrade Admin · Accepted Answer

Correct answer is (b) e prime=(√5/3)

Q. An ellipse $E$ has its centre $C (1, 3)$ focus at $S (6, 3)$ and passing through the point $P (4, 7)$ then
If the normal at a variable point on the ellipse (E) meets its axes in $Q$ and $R$ then the locus of the mid point of $QR$ is a conic with an eccentricity $(e^{'})$ , then -

$e^{'} = \frac{3}{10}$

$e^{'} = \frac{5}{3}$

$e^{'} = \frac{3}{5}$

$e^{'} = \frac{10}{3}$

Correct answer is (b) $e^{'} = \frac{5}{3}$

Q. An ellipse E has its centre C(1,3) focus at S(6,3) and passing through the point P(4,7) then If the normal at a variable point on the ellipse (E) meets its axes in Q and R then the locus of the mid point of QR is a conic with an eccentricity (e′), then -

e′=10​3​

e′=35​​

e′=5​3​

e′=310​​