Question

The focal distance of a point $(x_1,y_1)$ on the parabola $y^2=12x$ is

• A. $x_1+3$
• B. $x_1+6$
• C. $y_1+6$
• D. $y_1+3$

Answer 1

The correct option is A $x_1+3$

$y^2=12x=4\times 3x$ is of the form $y^2=4ax$ where $a=3$

$\therefore$ focus of a parabola is $(a,0)\equiv (3,0)$

Focal distance$=$Distance between $(x_1,y_1)$ and $(3,0)$

Using distance formula we have

Focal distance$=\sqrt{{(x_1-3)}^2+{(y_1-0)}^2}$

$=\sqrt{x_1^2+y_1^2-6x_1+9}$