Square of the area of the triangle formed by end points of a focal chord P Q of length 32 units of the parabola y2=8 x and its vertex is

Question

Square of the area of the triangle formed by end points of a focal chord P Q of length 32 units of the parabola y2=8 x and its vertex is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P Q=2(t+(1/t))2=32 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2d690905977c4b7e51faf5a87629bb6d-.png" /> t+(1/t)=4,-4 Area of Δ O P Q is =(1/2)|2 t2 4 t 1 (2/t2) -(4/t) 1 0 0 1| |(1/2)(-(8/t)-8 t)|=16

Q. Square of the area of the triangle formed by end points of a focal chord $PQ$ of length $32$ units of the parabola $y^{2} = 8 x$ and its vertex is

$PQ = 2 (t + \frac{1}{t})^{2} = 32$

$t + \frac{1}{t} = 4, - 4$
Area of $Δ OPQ$ is $= \frac{1}{2} ∣ ∣ 2 t^{2} \frac{2}{t ^{2}} 0 4 t - \frac{4}{t} 0 111 ∣ ∣$
$∣ ∣ \frac{1}{2} (- \frac{8}{t} - 8 t) ∣ ∣ = 16$

Q. Square of the area of the triangle formed by end points of a focal chord PQ of length 32 units of the parabola y2=8x and its vertex is

PQ=2(t+t1​)2=32 t+t1​=4,−4 Area of ΔOPQ is =21​∣∣​2t2t22​0​4t−t4​0​111​∣∣​ ∣∣​21​(−t8​−8t)∣∣​=16

Q. Square of the area of the triangle formed by end points of a focal chord $PQ$ of length $32$ units of the parabola $y^{2} = 8 x$ and its vertex is

$PQ = 2 (t + \frac{1}{t})^{2} = 32$

$t + \frac{1}{t} = 4, - 4$
Area of $Δ OPQ$ is $= \frac{1}{2} ∣ ∣ 2 t^{2} \frac{2}{t ^{2}} 0 4 t - \frac{4}{t} 0 111 ∣ ∣$
$∣ ∣ \frac{1}{2} (- \frac{8}{t} - 8 t) ∣ ∣ = 16$