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Question

Equation of the parabola with focus (3,4) and directrix x+y+7=0 is

A
x2+y22xy26x+2y+1=0
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B
x2+y22xy26x+4y3=0
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C
x2+y22xy26x+14y3=0
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D
x2+y22xy26x2y+5=0
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Solution

The correct option is A x2+y22xy26x+2y+1=0
Let point P(x,y) on parabola then from the definition of a parabola

PS=Distance of point P from focus.

PM=Distance of point P from the directrix.

PS=PM

(x3)2+(y+4)2=∣ ∣1.x1.y+712+12∣ ∣

(x3)2+(y+4)2=(x+y+7)22

2(x2+96x+y2+16+8y)=x2+y2+49+2xy+14x+14y

x2+y22xy26x+2y+1=0

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