The locus of the mid point of the focal radii of a variable point moving on the parabola, y2=4 a x is a parabola whose

Question

The locus of the mid point of the focal radii of a variable point moving on the parabola, y2=4 a x is a parabola whose (A) Latus rectum is half the latus rectum of the original parabola (B) Vertex is (a / 2,0) (C) Directrix is y-axis (D) All of these

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/1138369479b380322b64aafb6d0c5f7c-.png" /> h =( a +α/2), k =(β/2) ⇒ α=2 h - a , β=2 k (α, β) satisfies the parabola ∴ β2=4 a α 4 k 2=4 a (2 h - a ) y 2= a (2 x - a ) y 2=2 a ( x -( a /2))

Q. The locus of the mid point of the focal radii of a variable point moving on the parabola, $y^{2} = 4 a x$ is a parabola whose

Latus rectum is half the latus rectum of the original parabola

Vertex is $(a /2, 0)$

Directrix is $y$ -axis

All of these

$h = \frac{a + α}{2}, k = \frac{β}{2}$
$\Rightarrow α = 2 h - a, β = 2 k$
$(α, β)$ satisfies the parabola
$∴ β^{2} = 4 a α$
$4 k^{2} = 4 a (2 h - a)$
$y^{2} = a (2 x - a)$
$y^{2} = 2 a (x - \frac{a}{2})$

Q. The locus of the mid point of the focal radii of a variable point moving on the parabola, y2=4ax is a parabola whose

Latus rectum is half the latus rectum of the original parabola

Vertex is (a/2,0)

Directrix is y-axis

All of these

h=2a+α​,k=2β​ ⇒α=2h−a,β=2k (α,β) satisfies the parabola ∴β2=4aα 4k2=4a(2h−a) y2=a(2x−a) y2=2a(x−2a​)

Q. The locus of the mid point of the focal radii of a variable point moving on the parabola, $y^{2} = 4 a x$ is a parabola whose

Vertex is $(a /2, 0)$

Directrix is $y$ -axis

$h = \frac{a + α}{2}, k = \frac{β}{2}$
$\Rightarrow α = 2 h - a, β = 2 k$
$(α, β)$ satisfies the parabola
$∴ β^{2} = 4 a α$
$4 k^{2} = 4 a (2 h - a)$
$y^{2} = a (2 x - a)$
$y^{2} = 2 a (x - \frac{a}{2})$