What is the equation of the quadratic graph with a focus of 6 0 and a Directrix of Y − 10?
What is the equation of the quadratic graph with a focus of 6 0 and a Directrix of Y − 10?
Answer: The equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10 is x2 -12x – 20y = 64. Let us see how we will use the concept of focal point and directrix to find the equation. Explanation: Given that, Focus = (6, 0) and directrix y = -10.
How do you find the standard form of a parabola when given the focus?
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 equation of the quadratic graph with a focus of 4 0 and a Directrix of Y 10?
Summary: The equation of the quadratic graph with a focus of (4,0) and a directrix of y=10 is (x-4)2= -20(y – 5).
How do I find the equation of a parabola?
How to find a parabola’s equation using its Vertex Form
- Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k.
- Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.
How do you find the equation of a parabola given the focus and Directrix?
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 the equation of a parabola with focus?
Therefore, the equation of the parabola with focus ( a, b) and directrix y = c is If the focus of a parabola is ( 2, 5) and the directrix is y = 3 , find the equation of the parabola. Let ( x 0, y 0) be any point on the parabola.
How do you find the directrix of a parabola?
If we consider only parabolas that open upwards or downwards, then the directrix will be a horizontal line of the form y = c . Let ( a , b ) be the focus and let y = c be the directrix. Let ( x 0 , y 0 ) be any point on the parabola.
How do you find the vertex between the focus and directrix?
The vertex ( h, k) ( h, k) is halfway between the directrix and focus. Find the x x coordinate of the vertex using the formula x = x coordinate of focus + directrix 2 x = x coordinate of focus + directrix 2. The y y coordinate will be the same as the y y coordinate of the focus. Simplify the vertex.