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Questions  >>  CBSE XI  >>  Math  >>  Conic Sections
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Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ y^2=12x$

$\begin {array} {1 1} (A)\;focus : (0,3), axis :y - axis , Equation \: of \: directrix : x - 3=0, length \: of \: the \: latucrectum : 12 \\ (B)\;focus : (3,0), axis : x - axis , Equation \: of \: directrix : x + 3=0, length \: of \: the \: latucrectum : 12 \\ (C)\;focus : (-3,0), axis : x - axis , Equation \: of \: directrix : x - 3=0, length \: of \: the \: latucrectum : 12 \\ (D)\;focus : (0,-3), axis : y - axis , Equation \: of \: directrix : x + 3=0, length \: of \: the \: latucrectum : 12 \end {array}$

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A)
Toolbox:
  • Equation of a parabola is $y^2=4ax$
  • If x is positive , then the parabola opens towards the right.
  • If the equation involves $y^2$ then the axis of the parabola is x - axis.
  • Equation of the directrix is x = -a or x+a=0
  • Length of the lactus rectum is 4a.
Step 1 :
The given equation is $y^2=12x$
Since the coefficient of x is positive, the parabola opens towards the right.
We know the equation of parabola is $y^2 = 4ax$
Comparing both the equations we get,
$4a=12$
$ \Rightarrow a=3$
$ \therefore $ The coordinates of focus is (3, 0)
The axis of the parabola is x - axis.
Equation of directrix is x = -3 or x+3=0
Length of the latus rectum is $ 4 \times 3 = 12$
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