Question

# Find the equation of the parabola whose vertex is $$(3, -2)$$ and focus is $$(3, 1)$$.

Solution

## Clearly we can see that axis of parabola is parallel to y-axisAssume the equation of parabola to be :$$(x-h) ^{2}=4b(y-k)$$Focus =$$(h, k+b) =(3, 1)$$Vertex $$=(h, k) =(3, - 2)$$$$\Rightarrow h=3,\,k=-2,\,b=3$$$$\Rightarrow$$equation of parabola is : $$(x-3)^{2}=12(y+2)$$Mathematics

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