Question

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

• A. $x^2+y^2-2xy-26x+2y+1=0$
• B. $x^2+y^2-2xy-26x+4y-3=0$
• C. $x^2+y^2-2xy-26x+14y-3=0$
• D. $x^2+y^2-2xy-26x-2y+5=0$

Answer 1

The correct option is A $x^2+y^2-2xy-26x+2y+1=0$

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.

$PS=PM$

$\sqrt{(x-3{)}^2+(y+4{)}^2}=\left|\frac{1.x-1.y+7}{\sqrt{1^2+1^2}}\right|$

$(x-3{)}^2+(y+4{)}^2=\frac{(x+y+7{)}^2}{2}$

$2(x^2+9-6x+y^2+16+8y)=x^2+y^2+49+2xy+14x+14y$

$x^2+y^2-2xy-26x+2y+1=0$