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Question

Equation of the parabola having focus $$(3,2)$$ and Vertex $$(-1,2)$$ is 


A
(x+1)2=16(y2)
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B
(x1)2=16(y+2)
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C
(y2)2=16(x+1)
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D
(y+2)2=16(x1)
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Solution

The correct option is C $$(y-2)^2=16(x+1)$$
Equation of a General Parabola having axis along the x-axis  is given by $$y^2=4ax$$

where $$a=$$ distance between Vertex and Focus.

Here $$y$$ coordinate in Focus and Vertex is the same.

Thus this parabola would be along direction of the x-axis.

Diatance between vertex and focus $$=\sqrt{(3-(-1))^2+(2-2)^2}=4$$

thus equation of parabola is $$(y-2)^2=4.(4)(x-(-1))$$

i.e.$$(y-2)^2=16(x+1)$$

Mathematics

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