Question

The focus of a parabola is located at (0,–2). The directrix of the parabola is represented by y = 2. Which equation represents the parabola? y2 = –2x x2 = –2y y2 = –8x x2 = –8y

Answer 1

according to definition of parabola, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

i.e., √{(x - a)² + (y - b)²} = |y - mx - c|/√(m² + 1) is equation of parabola, if y = mx + c is directrix and (a,b) is parabola.

given, directrix : y = 2 => y = 0.x + 2

focus : (0, -2)

so equation of parabola,

√{(x - 0)² + (y + 2)²} = |y - 2 |/√(0 + 1)

or, √{x² + (y + 2)²} = (y - 2)²

squaring both sides,

x² + (y + 2)² = (y - 2)²

or, x² + y² + 4y + 4 = y² - 4y + 4

or, x² = -8y

hence, equation of parabola is x² = -8y

Answer 2

Answer:

D) x2 = –8y

Step-by-step explanation: