Question

What is the directrix of the following graph?
X = -3
Y= 3
Y = -3
X = 3

Answer 1

y = 3

Explanation:

The vertex of the parabola is (1,4) and the axis of the parabola is parallel to the positive y-axis.

So, the equation of the parabola will be (x - 1)² = 4a(y - 4) ....... (1)

Now, we have to get the value of a since the equation id the directrix is y = 4 - a.

Now, the parabola passes through the point (3,5) {Obtained from the graph).

Therefore, from equation (1), we get, 2² = 4a × 1, ⇒a = 1

Therefore, the equation of the directrix is y = 4 - 1 = 3. (Answer)