Q. 45.0( 2 Votes )

# Write the equation of the parabola with focus (0, 0) and directrix x + y – 4 = 0.

Answer :

Given that we need to find the equation of the parabola whose focus is S(0, 0) and directrix(M) is x + y - 4 = 0.

Let us assume P(x, y) be any point on the parabola.

We know that the point on the parabola is equidistant from focus and directrix.

We know that the distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is .

We know that the perpendicular distance from a point (x_{1}, y_{1}) to the line ax + by + c = 0 is .

⇒ SP = PM

⇒ SP^{2} = PM^{2}

⇒

⇒

⇒

⇒ 2x^{2} + 2y^{2} = x^{2} + y^{2} - 8x - 8y + 2xy + 16

⇒ x^{2} + y^{2} - 2xy + 8x + 8y - 16 = 0

∴The equation of the parabola is x^{2} + y^{2} - 2xy + 8x + 8y - 16 = 0.

Rate this question :

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

RD Sharma - MathematicsThe equation of the parabola whose focus is (1, - 1) and the directrix is x + y + 7 = 0 is

RD Sharma - MathematicsFind the equation of the parabola, if

the focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x – y = 3

RD Sharma - MathematicsFind the equation of the parabola, if

the focus is at (0, - 3) and the vertex is at (- 1, - 3)

RD Sharma - MathematicsFind the equation of the parabola, if

the focus is at (- 6, 6) and the vertex is at (- 2, 2)

RD Sharma - MathematicsWrite the equation of the parabola whose vertex is at (- 3, 0) and the directrix is x + 5 = 0.

RD Sharma - MathematicsWrite the coordinates of the vertex of the parabola whose focus is at (- 2, 1) and directrix is the line x + y – 3 = 0.

RD Sharma - MathematicsIf the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

RD Sharma - MathematicsFind the equation of the parabola whose focus is (5, 2) and having a vertex at (3, 2).

RD Sharma - MathematicsWrite the equation of the parabola with focus (0, 0) and directrix x + y – 4 = 0.

RD Sharma - Mathematics