Question

Find the vertex, axis, focus, directrix, length of latus rectum of the parabola x² + 2y – 3x + 5 = 0. Answer: Vertex = (3/2, -11/8), Focus = (3/2, -15/8), Directrix = y = -7/8, length of latus rectum = 2​

Answer 1

To find the vertex, axis, focus, directrix, and length of the latus rectum of the parabola x² + 2y – 3x + 5 = 0,

we can complete the square and then use the standard form of a parabola:

y = a(x - h)² + k

Start by completing the square:

x² - 3x + y2 + 5 = 0

x² - 3x + (3/2)² + 2y2 - 2*(3/2)2y + y2 + 5 = 0

$(x - 3/2)^2 + 2(y - (-11/8))^2 = -7/8$

Now we can see that the vertex of the parabola is$(3/2, -11/8).$

The axis of the parabola is the line$x = 3/2,$ since the vertex is in the form (h, k).

The focus of the parabola is at the point $(3/2, -15/8)$ since the coefficient of (y - k)² is 2.

The directrix of the parabola is the line y = -7/8, since the constant term of the equation is -7/8.

The length of the latus rectum is 2, since the coefficient of (x - h)² is 1.

So the vertex, axis, focus, directrix, and length of latus rectum of the parabola x² + 2y – 3x + 5 = 0 are:

Vertex = (3/2, -11/8)

Focus = (3/2, -15/8)

Directrix = y = -7/8

length of latus rectum = 2

Know more from the following links.

brainly.in/question/16766451

brainly.in/question/4211888

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