Find the standard equation of the parabola with the vertex (3,2) and the directrix y = - 2. Also find the length of the latus rectum of the parabola. Find the standard equation and write it in the form (y - k)? = c(x- h) or (x - h)2 = c(y - k) wherec = 4a or c= - 4a. O A. |(v- - 2 O B. (y-D? -> Ос. (х- = - OD. (v-D= -I(x-D What is the length of the latus rectum of the parabola?

Q: Nhat is the equation of the parabola containing the points (2, 2), (4,-8), and (-2, –14)? O y = - 4x…

A:

Q: Find an equation of the parabola with vertex (-2,-4) and directrix y=-9.

A: given vertex (h,k)=(-2,-4) h=-2,k=-4 directrix y=k-p=-9                  p=k+9                p=-4+9…

Q: Write the equation of the parabola given by y? + 2y + 12x – 23 = 0 in standard form. %3D -

A: Given equation of parabola is y2 + 2y + 12x - 23 = 0

Q: Write the equation of the parabola that has the same shape as f(x) = - 6x? but with vertex ( - 5,3)…

A: In this question we have to write the equation of the parabola that has the same shape as f(x)=-6x2…

Q: A parabola is defined by the equation y=x2+2x+3. Write equations of the tangents to the parabola…

A: Given the equation of parabola:

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: 66. One parabola at the right has the equation y-&-4)+ 2. Which equation represents the second…

A: Solution is given as below:

Q: Determine the equation of a parabola whose zeros are 2 and -11 and whose graph passes through the…

A: The zeros of the parabola are 2 and -11 and the graph passes through the point (3, 84). Let the…

Q: A parabola has a vertex at (4,-11) and runs through the point (8,-123). Determine the equation for…

A:

Q: True or False The equation 3x2 + Bxy + 12y2 = 10defines a parabola if B = - 12.

A: It is known that ax2+bxy+cy2+d=0 represents the parabola if b2-4ac=0.

Q: 6) Write an equation of the parabola with the vertex (3, -1) and the focus (3, -5).

A: Equation of parabola is

Q: Determine the equation of the parabola with vertex (2,8) and x-intercepts 0 and 4 in factored form…

A:

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: Write the standard equation of each parabola. Find the focus and make a graph. (i) passes through…

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Q: Vhich of these quadratics results in the skinniest parabola? O y = 4(x – 3)² +7 O y = -6(x+ 1)² O y…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.