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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-axis
Assume 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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