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Question

If the focus of a parabola is (2,5) and the directrix is y=3, the equation of the parabola is

A
x2+4x+4y+20=0
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B
x2+4x4y+20=0
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C
x24x4y+20=0
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D
x2+4x+4y+10=0
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Solution

The correct option is C x24x4y+20=0
Let (x,y) be any point on the parabola then the distance of this point from focus is equal to distance from directrix.

Distance of point from focus =(x2)2+(y5)2
Distance of point from directrix =|0.x+1.y3|12+02

(x2)2+(y5)2=|y3|
squaring both sides, we get
(x2)2+(y5)2=(y3)2
x24x+4+y210y+25=y26y+9
x24x4y+20=0

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