If the locus of middle point of point of contact of tangent drawn to the parabola y2=8 x and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic.

Question

If the locus of middle point of point of contact of tangent drawn to the parabola y2=8 x and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/af6096fa4cb203ed9340c312a4d5aa5d-.png" /> ( h , k ) is mid point of PT then ⇒ 2 h = a ⋅ (4 k 2/9 a 2) ⇒ 2 y 2=9 ax a =2 y2=9 x text L.R =9

Q. If the locus of middle point of point of contact of tangent drawn to the parabola $y^{2} = 8 x$ and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic.

$(h, k)$ is mid point of PT then
$\Rightarrow 2 h = a \cdot \frac{4 k ^{2}}{9 a ^{2}}$
$\Rightarrow 2 y^{2} = 9 a x$
$a = 2$
$y^{2} = 9 x$
$L.R = 9$

Q. If the locus of middle point of point of contact of tangent drawn to the parabola y2=8x and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic.

(h,k) is mid point of PT then ⇒2h=a⋅9a24k2​ ⇒2y2=9ax a=2 y2=9x L.R =9

Q. If the locus of middle point of point of contact of tangent drawn to the parabola $y^{2} = 8 x$ and the foot of perpendicular drawn from its focus to the tangent is a conic then find the length of latus rectum of the conic.

$(h, k)$ is mid point of PT then
$\Rightarrow 2 h = a \cdot \frac{4 k ^{2}}{9 a ^{2}}$
$\Rightarrow 2 y^{2} = 9 a x$
$a = 2$
$y^{2} = 9 x$
$L.R = 9$