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Question

Coordinates of parametric point on the parabola, whose focus is (32,3) and the directrix is 2x+5=0 is given by

A
(2t2+2,2t3)
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B
(12t22,t3)
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C
(12t22,t+3)
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D
(12t2+2,t+3)
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Solution

The correct option is B (12t22,t3)
(x+32)2+(y+3)2=(2x+52)24[x2+94+3x]+4[y2+9+6y]=(4x2+25+20x)(y2+6y+9)2(x+2)=0
or (y+3)2=2(x+2)
Here a=12
Therefore x=12t22 and y=t3 satisfy it for all t.

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