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-...
How does one write a quadratic equation using the directrix and focus? With the given focus and directrix, determine the vertex of the parabola. Substitute the obtained vertex in the vector form of parabola. Again, with the values of {eq}a {/eq}, the quadratic equation is obtained. How ...
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 ...
The equation of the parabola with the focus (3,0) and directrix x+3=0 is Ay2=2x By2=3x Cy2=6x Dy2=12xSubmit Question 2 - Select One 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...
Step 2:Find {eq}h, k {/eq}, and {eq}p {/eq} using the equation of the parabola {eq}{(x-h)}^2=4p(y-k) {/eq} or {eq}{(y-k)}^2=4p(x-h) {/eq} Step 3:Find the focus and directrix of the parabola using the equations. ...
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 ...
Find the equation of the hyperbola whose : focus is (2,2) directrix isx+y=9and eccentricity=2. View Solution Find the equation of the parabola whose focus is (6, 0) and directrix isx=−6. View Solution Find the focus and the equation of the parabola whose vertex is(6,−3)and...
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 ...
A parabola is an essential component of the conic section, in which we discuss its numerous properties and equations. When we require the vertex, the equation of the directrix, and the focus, we should modify the given equation, keeping the general equ...
The equation of the parabola when its focus {eq}(p,q) {/eq} and the equation of the directrix {eq}y = l {/eq} are given, is found with the help of the standard equation of the parabola as given below: {eq}\left ( y-k \right )^{...