Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

Question

A. y = -1/7*x^2

B. y^2 = -7x

C. y = -1/28*x^2

D. y^2 = -28x

Answer 1

Step 1:

Vertex of the parabola is and focus is .

Observe the vertex and focus points, the coordinates are same and on axis.

Thus, the parabola is vertical.

Standard form of the parabola with vertex and focus is is .

The directrix is .

Compare the points and with the standard form.

Therefore, .

Substitutue in the .

Standard form of the parabola is .

Rewrite the equation .

Thus, option (c) is correct.

Solution:

Standard form of the parabola is .

Thus, option (c) is correct.