Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P. (4, -4) Q (9, 6). Let R be a point on the arc of the parabola between P Q. Then the area of Δ PQR is largest when

Question

Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P. (4, -4) Q (9, 6). Let R be a point on the arc of the parabola between P Q. Then the area of Δ PQR is largest when (A)  angle PQR = 90° (B) R (4,4) (C) R ( (1/4) , 1 ) (D) R ( 1, (1/4) )

Tardigrade Admin · Accepted Answer

Equation of PQ is 2x - y = 12 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/1965f24675de665cf2a58a0429f5775a-.png" /> Perpendicular distance L R=|(2 t2-2 t-12/√5)| =(2/√5)(t-3)(t+2) L R is Maximum, at t=(1/2) ∴ R is ((1/4), 1)

Q. Consider the parabola $y^{2} = 4 x$ . Let $P$ and $Q$ be points on the parabola where $P . (4, - 4)$ & $Q (9, 6)$ . Let $R$ be a point on the arc of the parabola between $P & Q$ . Then the area of $Δ$ PQR is largest when

$∠ PQR = 9 0^{\circ}$

$R (4, 4)$

$R (\frac{1}{4}, 1)$

$R (1, \frac{1}{4})$

Equation of $PQ$ is $2 x - y = 12$

Perpendicular distance
$L R = ∣ ∣ \frac{2 t ^{2} - 2 t - 12}{5} ∣ ∣$
$= \frac{2}{5} (t - 3) (t + 2)$
$L R$ is Maximum, at $t = \frac{1}{2}$
$∴ R$ is $(\frac{1}{4}, 1)$

Q. Consider the parabola y2=4x. Let P and Q be points on the parabola where P.(4,−4) & Q(9,6). Let R be a point on the arc of the parabola between P&Q. Then the area of ΔPQR is largest when

∠PQR=90∘

R(4,4)

R(41​,1)

R(1,41​)