Question

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

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

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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