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Question

Equation of the parabola whose vertex is $$(-3,-2)$$, axis is horizontal and which passes through the point $$(1,2)$$ is


A
y2+4y+4x8=0
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B
y2+4y4x+8=0
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C
y2+4y4x8=0
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D
None of these
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Solution

The correct option is B $${ y }^{ 2 }+4y-4x-8=0$$
Since the axis is horizontal and vertex is $$(-3,-2)$$
$$\therefore$$ the equation of the parabola must be of the form $${ \left( y+2 \right)  }^{ 2 }=4a\left( x+3 \right) $$
It passes through $$(1,2)$$, so $$16=16a$$
$$\Rightarrow a=1$$
Hence, the equation of the parabola is
$${ \left( y+2 \right)  }^{ 2 }=4\left( x+3 \right)$$
$$ \Rightarrow { y }^{ 2 }+4y-4x-8=0$$

Mathematics

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