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 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-...
The coefficient a in the quadratic equation determines the direction in which the parabola opens. If the coefficient is positive, it opens upward; if negative, the parabola opens downward. 5. Focus and Directrix In the context of conic sections, the focus is a fixed point through which all ...
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 ...
Learn to find the equation of a parabola with examples. Understand the equation of a parabola in standard form and the properties and applications...
Exploring Focus/Directrix relation to Graph You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y = .1x² is a wider parabola than y = .2x² and y = -.1x² is a wider parabola than y = .-2x². You...
Find the equation of the parabola with focus at (3, -4) and directrix x + y - 2 = 0 . Ax2+4xy+y2−8x+20y+46=0 Bx2+2xy+y2−8x+20y+46=0 Cx2−2xy+y2−8x+20y+46=0 Dx2−4xy+y2−8x+20y+46=0Submit Question 3 - Select One Equation of parabola with focus (0...
We can generalize and write the equation of a parabola at a vertex V(h,k) as follows y=14p(x−h)2+k with vertex V(h,k) and focus F(h,k+p) and directrix given by the equation y=k−p Example 2 Find the vertex, focus and directrix of the parabola given by the equation ...
Directrix 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 the parabola, it must...
The simplest equation for a parabola isy = x2 Turned on its side it becomesy2= x (ory = √xfor just the top half) A little more generally: y2= 4ax whereais the distance from the origin to the focus (and also from the origin to directrix) ...