The points A(3 , 6) and B lie on the parabola y2=4ax , such that the chord AB subtends 90° at the origin, then the length of the chord AB is equal to

Question

The points A(3 , 6) and B lie on the parabola y2=4ax , such that the chord AB subtends 90° at the origin, then the length of the chord AB is equal to (A) 15√13 units (B) 12√17 units (C) 9√17 units (D) 9√10 units

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-50oqob5ekrro.png" /> Since the chord subtends a right angle at the origin, ∴ t1t2=-4 Now, the point A lies on the parabola, ∴ 36=4a(3)⇒ a=3 i.e. A(3 , 6)=(3 t12 , 6 t1) ⇒ t1=1⇒ t2=-4 So, B≡ (48 , - 24) Hence, the length of the chord AB=15√13 units

Q. The points $A (3, 6)$ and $B$ lie on the parabola $y^{2} = 4 a x$ , such that the chord $A B$ subtends $9 0^{\circ}$ at the origin, then the length of the chord $A B$ is equal to

$1513$ units

$1217$ units

$917$ units

$910$ units

Q. The points A(3,6) and B lie on the parabola y2=4ax , such that the chord AB subtends 90∘ at the origin, then the length of the chord AB is equal to

1513​ units

1217​ units

917​ units

910​ units

Since the chord subtends a right angle at the origin, ∴t1​t2​=−4 Now, the point A lies on the parabola, ∴36=4a(3)⇒a=3 i.e. A(3,6)=(3t12​,6t1​) ⇒t1​=1⇒t2​=−4 So, B≡(48,−24) Hence, the length of the chord AB=1513​ units

Q. The points $A (3, 6)$ and $B$ lie on the parabola $y^{2} = 4 a x$ , such that the chord $A B$ subtends $9 0^{\circ}$ at the origin, then the length of the chord $A B$ is equal to

$1513$ units

$1217$ units

$917$ units

$910$ units