Let the normals at points A(4 a , - 4 a) and B(9 a , - 6 a) on the parabola y2=4ax meet at the point P. The equation of the normal from P on y2=4ax (other than PA and PB ) is

Question

Let the normals at points A(4 a , - 4 a) and B(9 a , - 6 a) on the parabola y2=4ax meet at the point P. The equation of the normal from P on y2=4ax (other than PA and PB ) is (A) 5x+y-135a=0 (B) 5x-y+115a=0 (C) 5x+y+115=0 (D) 5x-y-115a=0

Tardigrade Admin · Accepted Answer

Let, A=(a t12 , 2 a t1), B=(a t22 , 2 a t2) and the foot of the required normal is (a t32 , 2 a t3) , then 2at1=-4a, 2at2=-6a and t1+t2+t3=0 ⇒ t1=-2, t2=-3 and -2-3+t3=0 ⇒ t3=5 Hence, the equation of the required normal is y=-t3x+2at3+at32 ⇒ y=-5x+10a+125a ⇒ y+5x-135a=0

Q. Let the normals at points $A (4 a, - 4 a)$ and $B (9 a, - 6 a)$ on the parabola $y^{2} = 4 a x$ meet at the point $P .$ The equation of the normal from $P$ on $y^{2} = 4 a x$ (other than $P A$ and $PB$ ) is

$5 x + y - 135 a = 0$

$5 x - y + 115 a = 0$

$5 x + y + 115 = 0$

$5 x - y - 115 a = 0$

Q. Let the normals at points A(4a,−4a) and B(9a,−6a) on the parabola y2=4ax meet at the point P. The equation of the normal from P on y2=4ax (other than PA and PB ) is

5x+y−135a=0

5x−y+115a=0

5x+y+115=0

5x−y−115a=0

Q. Let the normals at points $A (4 a, - 4 a)$ and $B (9 a, - 6 a)$ on the parabola $y^{2} = 4 a x$ meet at the point $P .$ The equation of the normal from $P$ on $y^{2} = 4 a x$ (other than $P A$ and $PB$ ) is

$5 x + y - 135 a = 0$

$5 x - y + 115 a = 0$

$5 x + y + 115 = 0$

$5 x - y - 115 a = 0$