The triangle PQR of area ' A ' is inscribed in the parabola y 2=4 ax such that the vertex P lies at the vertex of the parabola and the base QR is a focal chord. The modulus of the difference of the ordinates of the points Q and R is -

Question

The triangle PQR of area ' A ' is inscribed in the parabola y 2=4 ax such that the vertex P lies at the vertex of the parabola and the base QR is a focal chord. The modulus of the difference of the ordinates of the points Q and R is - (A) ( A /2 a ) (B) ( A / a ) (C) (2 A / a ) (D) (4 A / a )

Tardigrade Admin · Accepted Answer

Since Q R is focal chord so vertex of Q is (at 12, 2 at 1 ) and R is ( at 22, 2 at 2) area of Δ PQR =(1/2)|0 0 1 at 12 2 at 1 1 at 22 2 at 2 1| A=(1/2)|2 a2 t12 t2-2 a2 t1 t22| A=(a/2)|2 at 1-2 a t2| [t1 t2=-1]

Q. The triangle PQR of area ' $A$ ' is inscribed in the parabola $y^{2} = 4 a x$ such that the vertex $P$ lies at the vertex of the parabola and the base $QR$ is a focal chord. The modulus of the difference of the ordinates of the points $Q$ and $R$ is -

$\frac{A}{2 a}$

$\frac{A}{a}$

$\frac{2 A}{a}$

$\frac{4 A}{a}$

Q. The triangle PQR of area ' A ' is inscribed in the parabola y2=4ax such that the vertex P lies at the vertex of the parabola and the base QR is a focal chord. The modulus of the difference of the ordinates of the points Q and R is -

2aA​

aA​

a2A​

a4A​

Since QR is focal chord so vertex of Q is (at 12​,2at1​ ) and R is (at22​,2at2​) area of ΔPQR=21​∣∣​0at12​at22​​02at1​2at2​​111​∣∣​ A=21​∣∣​2a2t12​t2​−2a2t1​t22​∣∣​ A=2a​∣2at1​−2at2​∣[t1​t2​=−1]

Q. The triangle PQR of area ' $A$ ' is inscribed in the parabola $y^{2} = 4 a x$ such that the vertex $P$ lies at the vertex of the parabola and the base $QR$ is a focal chord. The modulus of the difference of the ordinates of the points $Q$ and $R$ is -

$\frac{A}{2 a}$

$\frac{A}{a}$

$\frac{2 A}{a}$

$\frac{4 A}{a}$