What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? pls

ANSWER


EXPLANATION

Since the directrix is


the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,



also means that the parabola will open upwards.

The equation of parabola with such properties is given by,


where


is the vertex of the parabola.

The directrix and the axis of symmetry of the parabola will intersect at


The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,


and


The equation of the parabola now becomes,





Thus, the distance between the vertex and the directrix.

This means that,



Since the parabola opens up, we choose

Our equation now becomes,



This simplifies to


or



This is the same as,



The correct answer is D .