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
B
y2+4y4x+8=0
C
y2+4y4x8=0
D
None of these

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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