Coordinates of parametric point on the parabola, whose focus is (−32,−3) and the directrix is 2x+5=0 is given by
A
(2t2+2,2t−3)
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B
(12t2−2,t−3)
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C
(12t2−2,t+3)
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D
(12t2+2,t+3)
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Solution
The correct option is B(12t2−2,t−3) (x+32)2+(y+3)2=(2x+52)2⇒4[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=12t2−2 and y=t−3 satisfy it for all t.