Length of the focal chord of the parabola y2 = 4ax at a distance p from the vertex is :

Question

Length of the focal chord of the parabola y2 = 4ax at a distance p from the vertex is : (A) (2a2/p) (B) (a3/p2) (C) (4a3/p2) (D) (p2/a)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2b55b5e0e603b7e6fc2e608c556915b1-.png" /> Length = √(2 at + (2a/1))2+(at2-(a/t2))2=(a(1+t2)2/t2) Now equation of focal chord, 2 tx + y (1 - t2) - 2 at = 0 ⇒|(2at/1+t2)|⇒(4a2/P2)=((1+t2)2/t2)

Q. Length of the focal chord of the parabola $y^{2} = 4 a x$ at a distance p from the vertex is :

$\frac{2 a ^{2}}{p}$

$\frac{a ^{3}}{p ^{2}}$

$\frac{4 a ^{3}}{p ^{2}}$

$\frac{p ^{2}}{a}$

Q. Length of the focal chord of the parabola y2=4ax at a distance p from the vertex is :

p2a2​

p2a3​

p24a3​

ap2​

Length = (2at+12a​)2+(at2−t2a​)2​=t2a(1+t2)2​ Now equation of focal chord, 2tx+y(1−t2)−2 at =0 ⇒∣∣​1+t22at​∣∣​⇒P24a2​=t2(1+t2)2​

Q. Length of the focal chord of the parabola $y^{2} = 4 a x$ at a distance p from the vertex is :

$\frac{2 a ^{2}}{p}$

$\frac{a ^{3}}{p ^{2}}$

$\frac{4 a ^{3}}{p ^{2}}$

$\frac{p ^{2}}{a}$