The slope of a chord of the parabola y2 = 4ax which is normal at one end and which subtends a right angle at the origin is

Question

The slope of a chord of the parabola y2 = 4ax which is normal at one end and which subtends a right angle at the origin is (A) ±(1/√2) (B) ±√2 (C) ± 2 (D) none of these.

Tardigrade Admin · Accepted Answer

The equation of a normal to the parabola,

y^{2} = 4 a x

is

t x + y = 2 a t + a t^{3}

If the normal chord makes a right angle at the vertex of the parabola, then

t^{2} = 2

∴ t = \pm 2

∴

slope of normal chord is

- t = \pm 2

Q. The slope of a chord of the parabola $y^{2} = 4 a x$ which is normal at one end and which subtends a right angle at the origin is

$\pm \frac{1}{2}$

$\pm 2$

$\pm 2$

none of these.

The equation of a normal to the parabola, $y^{2} = 4 a x$
is $t x + y = 2 a t + a t^{3}$
If the normal chord makes a right angle at the vertex of the parabola, then
$t^{2} = 2$
$∴ t = \pm 2$
$∴$ slope of normal chord is $- t = \pm 2$

Q. The slope of a chord of the parabola y2=4ax which is normal at one end and which subtends a right angle at the origin is

±2​1​

±2​

±2

none of these.

The equation of a normal to the parabola, y2=4ax is tx+y=2at+at3 If the normal chord makes a right angle at the vertex of the parabola, then t2=2 ∴t=±2​ ∴ slope of normal chord is −t=±2​

Q. The slope of a chord of the parabola $y^{2} = 4 a x$ which is normal at one end and which subtends a right angle at the origin is

$\pm \frac{1}{2}$

$\pm 2$

$\pm 2$

The equation of a normal to the parabola, $y^{2} = 4 a x$
is $t x + y = 2 a t + a t^{3}$
If the normal chord makes a right angle at the vertex of the parabola, then
$t^{2} = 2$
$∴ t = \pm 2$
$∴$ slope of normal chord is $- t = \pm 2$