The directrix of a parabola is an imaginary straight line perpendicular to the axis that passes through the focus of the parabola. The equation for this line is y=d, where d is equal to the distance between the focus and directrix. This means that when we look at any given point on ...
Learn to find the equation of a parabola given its focus and directrix. Understand the standard equation of a parabola and learn to solve related...
The latus ractum of a parabola whose directrix is x+y−2=0 and focus is (3,−4), is A2√2 B3√2 C6√2 D3√2Submit Question 2 - Select One Equation of parabola with focus (0,2) and directrix y + 2 = 0 is Ax2=8y Bx2=2y Cx2=4y Dy2=4xSubmit Equation of the para...
Parabola Directrix Examples directrix(y−2)=3(x−5)2 directrix3x2+2x+5y−6=0 directrixx=y2 Related Symbolab blog posts Practice, practice, practice Math can be an intimidating subject. Each new topic we learn has symbols and problems we have never seen. The unknowing......
The coordinates of the focus is represented as $$f(-p,0) $$ while the equation of the directrix is given by $$x = p $$ Answer and Explanation:1 First, rewrite the given equation of the parabola: $$\begin{align} y^{2} + 12x & = 0 \\[0...
A parabola is the locus of a point that is equidistant from a fixed line called the directrix, and a fixed point called the focus of the parabola. The standard form of the equation of a parabola is {eq}(x-h)^2=4a(y-k) {/eq}, where the focus is {eq}(h,k+...
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. ...
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...
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 ...
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 ...