Tag: parabola

Questions Related to parabola

Multiple choice mathematics and statistics parabola tracing of the parabola definitions related to parabola introduction to parabola

The focus of the parabola $y ^ { 2 } = 4 y - 4 x$ is

  1. $( 0,2 )$
  2. $( 1,2 )$
  3. $( 4,2 )$
  4. $( 1,3 )$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow y^2 = 4y - 4x$

$\Rightarrow y^2 - 4y = -4x$
$\Rightarrow y^2 - 4y + 4 = -4x + y$
$\Rightarrow (y - 2)^2 = -4 (x - 1)$
vertex = $(1, 2)$
$\dfrac{1}{4 p} = \dfrac{-1}{4} \rightarrow p = -1$
$\therefore$ Focus = $(-1 + 1, 2 + 0) = (0, 2)$

Multiple choice mathematics and statistics parabola tracing of the parabola definitions related to parabola introduction to parabola

The equation of the directrix of the parabola, $y ^ { 2 } + 4 y + 4 x + 2 = 0$ is -

  1. $x = - 1$
  2. $x = 1$
  3. $x = - \dfrac {3 }{ 2}$
  4. $x = \dfrac {3 }{ 2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given equation of parabola
$y^2+4y+4x+2=0$
or $(y+2)^2+4x+2=0$
or $(y+2)^2=-4(x-12)$
Its directrix  is x12x−12=1=1
or x=32
Hence D is the correct answer.

y2+4y+4x+2=