Find the equation of the parabola whose focus is `(0,0)` and the vertex is the point of intersection of the lines `x+y=1` and `x - y = 3.`

Explanation

We need to find the equation of the parabola whose focus is (0, 0) and vertex is the point of intersection of lines `x + y = 1` and `x - y = 3`.

On solving the lines, we get the vertex `(2, - 1)`.

We know that, The line passing through focus and vertex i.e., the axis is perpendicular to the directrix and vertex is the midpoint of focus and point that lies at the intersection of axis and directrix.

` implies` Slope of axis as

`(m_1) = (− 1 − 0 )/(2 − 0 )`

`implies m_1 = − 1/2`

We know that, The products of the slopes of the perpendicular lines is - 1.

Let us assume m2 be the slope of the directrix.

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