The equation of the parabola with focus (0, 0 | vedclass

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Question

(A) By definition,a parabola is the locus of a point $P(x, y)$ such that its distance from the focus $S(0, 0)$ is equal to its perpendicular distance

Vedclass · Accepted Answer

$x^2 + y^2 - 2xy + 8x + 8y - 16 = 0$

Vedclass · Answer

(A) By definition,a parabola is the locus of a point $P(x, y)$ such that its distance from the focus $S(0, 0)$ is equal to its perpendicular distance from the directrix $x + y - 4 = 0$.$SP = PM \implies SP^2 = PM^2$$x^2 + y^2 = \left( \frac{x + y - 4}{\sqrt{1^2 + 1^2}} \right)^2$$x^2 + y^2 = \frac{(x + y - 4)^2}{2}$$2(x^2 + y^2) = x^2 + y^2 + 16 + 2xy - 8x - 8y$$x^2 + y^2 - 2xy + 8x + 8y - 16 = 0$

The equation of the parabola with focus $(0, 0)$ and directrix $x + y = 4$ is

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