Step 1:Identify the given equation and determine orientation of the parabola. Step 2:Findh,k, andpusing the equation of the parabola(x−h)2=4p(y−k)or(y−k)2=4p(x−h) Step 3:Find the focus and directrix of the parabola using the equations. ...
Find the vertex, focus, and directrix of the parabola. Then sketch the parabola. y=14(x2−2x+5) The Directrix of a Parabola Whenever we are given a quadratic function such as the one we are given in the equation, we can generate the graph of the...
Find the vertex, focus, and directrix of the parabola. Parabola The curve which is obtained by the intersection of a surface plane with the solid cone is called a conic section. The conic section is a parabola when a plane parallel to the generating line of the solid cone cuts the solid...
To find the vertex, focus, and directrix of the parabola given by the equation 4y2+12x−20y+67=0, we will follow these steps: Step 1: Rearranging the equationStart by rearranging the equation to isolate the terms involving y on one side. 4y2−20y+12x+67=0 Step 2: Grouping the ...
Since the directrix is vertical, use the equation of a parabola that opens up or down. ( ((x-h))^2=4p(y-k)) Find the vertex. ( (3,3)) Find the distance from the focus to the vertex. ( p=2) Substitute in the known values for the variables into the equation( ((x-h...
Answer to: Find the vertex, focus, and directrix of the parabola, and sketch its graph. (y - 2)^2 = 2x + 1 By signing up, you'll get thousands of...
Since thedirectrixisvertical, use theequationof aparabolathat opens up or down. (x−h)2=4p(y−k)(x-h)2=4p(y-k) Find thevertex. Tap for more steps... The(h,k)is halfway between theand. Find theyof theusing they=y coordinate of focus+directrix2. Thexwill be the same as ...
(x−h)2=4p(y−k)(x-h)2=4p(y-k)求顶点。 点击获取更多步骤... (0,0)(0,0)求从焦点到顶点的距离。 点击获取更多步骤... p=4p=4将变量的已知值代入方程 (x−h)2=4p(y−k)(x-h)2=4p(y-k)。 (x−0)2=4(4)(y−0)(x-0)2=4(4)(y-0)化简...
The distance from the focus (2, 1) to the directrix x=-4 is 2-(-4)=6, so the distance from the focus to the vertex is 12(6)=3 and the vertex is (-1, 1). Since the focus is to the right of the vertex, p=3. An equation is (y-1)^2=4⋅ 3[x-(-1)], or (y-...
To find the vertex and length of the latus rectum of the parabola given by the equation x2=−4(y−a), we can follow these steps: Step 1: Identify the standard form of the parabolaThe given equation can be rewritten in the standard form of a parabola that opens downwards. The stand...