The focal distance of a point on the parabola y 2=12 x is 4 . What is the abscissa of the point?

Question

The focal distance of a point on the parabola y 2=12 x is 4 . What is the abscissa of the point? (A) 1 (B) -1 (C) 2 √3 (D) -2

Tardigrade Admin · Accepted Answer

Focal distance of a point (x1, y1) on the parabola is y 2=4 ax is equal to its distance from directrix x + a =0 is x 1+1 For y 2=12 x ; a =3, so x 1+3=4 ⇒ x 1=1

Q. The focal distance of a point on the parabola $y^{2} = 12 x$ is 4 . What is the abscissa of the point?

1

-1

$23$

-2

Focal distance of a point $(x_{1}, y_{1})$ on the parabola is $y^{2} = 4 a x$ is equal to its distance from directrix
$x + a = 0$ is $x_{1} + 1$
For $y^{2} = 12 x; a = 3$ , so $x_{1} + 3 = 4 \Rightarrow x_{1} = 1$

Q. The focal distance of a point on the parabola y2=12x is 4 . What is the abscissa of the point?

1

-1

23​

-2

Focal distance of a point (x1​,y1​) on the parabola is y2=4ax is equal to its distance from directrix x+a=0 is x1​+1 For y2=12x;a=3, so x1​+3=4⇒x1​=1

Q. The focal distance of a point on the parabola $y^{2} = 12 x$ is 4 . What is the abscissa of the point?

$23$

Focal distance of a point $(x_{1}, y_{1})$ on the parabola is $y^{2} = 4 a x$ is equal to its distance from directrix
$x + a = 0$ is $x_{1} + 1$
For $y^{2} = 12 x; a = 3$ , so $x_{1} + 3 = 4 \Rightarrow x_{1} = 1$