What are the vertex focus and directrix of the parabola with the given equation y 1 28?

The vertex, focus and directrix of the parabola with the given equation y = 1/28(x - 4)² - 5 is (4, -5), (4, 2) and -12.

How do you find the vertex focus and directrix of a parabola given the equation?

The standard form is (x - h)² = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

What is the vertex focus and directrix of parabola?

The fixed-line is the directrix of the parabola and the fixed point is the focus denoted by F. The axis of the parabola is the line through the F and perpendicular to the directrix. The point where the parabola intersects the axis is called the vertex of the parabola.

Which equation represents a parabola with a focus of 0 1 and a Directrix of Y 1?

Summary: The equation of the parabola with a focus at (0, 1) and a directrix of y = -1 is x² = 4y.

Which equation represents a parabola with a focus of 0 4 and a Directrix of 2?

Summary: The equation y = (x²/4) + 3 represents a parabola with a focus of (0, 4) and a directrix of y = 2.

Finding The Focus and Directrix of a Parabola - Conic Sections

Which is the equation of a parabola with vertex 0 0 and focus (- 3 0 )? Acbd?

Summary: The equation of a parabola with vertex (0, 0) and focus (-3, 0) is y² = -12x.

How do you find the focus of a parabola with an equation?

In order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x−h)2+k where a represents the slope of the equation. From the formula, we can see that the coordinates for the focus of the parabola is (h, k+1/4a).

What is the formula for the focus of a parabola?

For the given equation of the parabola we first need to find the vertex, the value of 'a', and the axis of the parabola, to find the focus of parabola. For a parabola of the form (x - h)² = 4a(y - k), the y-axis is the axis of the parabola, the vertex is (h, k), and the focus of parabola is (h, k + a).

Which is the Directrix of a parabola with equation?

The directrix of a parabola can be found, by knowing the axis of the parabola, and the vertex of the parabola. For an equation of the parabola in standard form y² = 4ax, with focus at (a, 0), axis as the x-axis, the equation of the directrix of this parabola is x + a = 0 .

Where is the Directrix of a parabola?

The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola. If the axis of symmetry of a parabola is vertical, the directrix is a horizontal line . If we consider only parabolas that open upwards or downwards, then the directrix is a horizontal line of the form y=c .

What is the vertex formula?

The vertex formula to find the vertex coordinates (h,k)= (-b/2a, -D/4a) from the standard equation y = ax² + bx + c, where D = b² - 4ac.

Which is the equation of a parabola with focus (- 5 3 and vertex (- 5 6 )?

The equation of a parabola with focus (-5, 3) and vertex (-5, 6) is (x + 5)² = 12(y - 6).

What is the equation of the parabola with vertex at 0 0 and focus at 0 2?

The equation of a parabola with vertex (0, 0) and focus (0, 2) is y = (1/8)x².

Which is the equation of a parabola with focus 0 5 and Directrix Y?

Summary: The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is y = x² /20.

Which of the following is the equation for a parabola with a focus at 0 4 and a Directrix at Y − 4?

The equation of the parabola with a focus at (0, -4) and a directrix of y = 4 is x² + 16y = 0.

How do you graph the focus and directrix of a parabola?

Let (x0,y0) be any point on the parabola. Find the distance between (x0,y0) and the focus. Then find the distance between (x0,y0) and directrix. Equate these two distance equations and the simplified equation in x0 and y0 is equation of the parabola.

How do you find directrices?

The directrix can be identified as the lines parallel to the latus rectum, and also the minor axis of the ellipse. The directrix of the ellipse are the lines drawn external to the ellipse and are perpendicular to the major axis of the ellipse.

What are the vertices foci and asymptotes of the hyperbola with equation 16x 2 4y 2 64?

The vertices, foci and asymptotes of the hyperbola with the equation 16x² - 4y² = 64 are (±2, 0), [±2√5, 0], (2x - y) = 0 and (2x + y) = 0 respectively.

How do you find the vertices and foci of an hyperbola given the equation?

Example: Locating a Hyperbola's Vertices and Foci

The hyperbola is centered at the origin, so the vertices serve as the y-intercepts of the graph. To find the vertices, set x=0 x = 0 , and solve for y y . Therefore, the vertices are located at (0,±7) ( 0 , ± 7 ) , and the foci are located at (0,9) ( 0 , 9 ) .

How do you find the Directrix and focus of an equation?

Focus & directrix of a parabola from the equation

So the focus is (h, k + C), the vertex is (h, k) and the directrix is y = k – C.

How do you find the Directrix of a hyperbola?

The directrix is the line which is parallel to y axis and is given by x=ae or a2c and here e=√a2+b2a2 and represents the eccentricity of the hyperbola. So x=3.2 is the directrix of this hyperbola.