Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y into the equation. x )-4 %3D

Q: 14. Which equation represents the given parabola? O y = -4(x – 4)² + 5 O y = }(x – 4)² + 5 O y =…

A: First option is correct.

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

A:

Q: a. Find the coordinates of the vertex of the parabola y = ax2 + bx + c, a ≠ 0. b. When is the…

A: given the coordinates of the vertex of the parabola y = ax2 + bx + c, a ≠ 0.

Q: For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the…

A: Consider the given equation of parabola:

Q: (b) Find the equation of the sphere in R³ that has the diameter from A(1, 2, -1) to B(5,-2,0).

A: Part (b):- Given co-ordinates of diameter are  A1, 2, -1   to   B5, -2,  0.

Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Find the point P on the parabola y = x closest to the point (57, 0). (х, у) y y = x? P 57

A: Given parabola y=x2 The distance between two points is found by d=x2-x12+y2-y12 let a,a2 be the…

Q: nd an equation of a sphere if one of its diameters has endpoints (54.

A:

Q: O. Determine the vertex of the parabola y = x? – 14 + 40 by completing the square.

A: The parabola is  y = x2 -14x + 40

Q: Given the general form of a parabola x2+6x-24y+4=0, what is the x coordinate the vertex? h=_____.

A:

Q: Which way does the parabola open? (x+ 3 =4 y + 5). h drwn e laft d ninht aun

A:

Q: Given isosceles trapezoid PAGE. A G T E C. If GD = 4x - 5, DE = 2x -3, find 1. x= 2. GE = 3. AP=

A:

Q: 3 Which equation is for the hyperbola? O x = a (y – k)² + h (z-h)² (y-k)? = 1 O (z – h)° + (y – k)°…

A: LET'S FIND HYPERBOLA EQUATION,   ANSWER :-  OPTION B IS RIGHT   OPTION A IS PARABOLA. OPTION C IS…

Q: Suppose (P, Q) is the point on the graph of y = Vx closest to (1, 0). What is the value of P+ Q?…

A: In this we have to find the closest distance and then sum up. So I'm providing hand written solution…

Q: Find the dimensions of the reclanyie uf iurg lying on the parabola. y = 6- x2 width units height…

A:

Q: E. Explain what a second-degree equation in tow variables, x and y, is, and how you can ell whether…

A: Please look into the next step for details

Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

A:

Q: What is the axis of symmetry of the parabola y=1/4x^2−14x+28?   A. y=28 B. x=7 C. x= -14 D. x=28

A: Given y=14x2-14x+28

Q: Suppose (P, Q) is the point on the graph of y=Vx closest to (1, 0). What is the value of P+ Q?…

A: Given: Point (P,Q) lies on y=x    Then (P,Q) satisfies y=x  then     Q=P Then P=Q2 Distance of point…

Q: The Vertex and the value of 'p' of the given parabola (x – 5)² = 16(y – 9) are

A:

Q: What is the equation of the parabola that opens to the right and with vertex at (4,-2) and a latus…

A: Prabola

Q: What is the directrix of the parabola? (x – 4)? = 8 (y + 3) O x = -3 O y = -3 y = -5 x = -5

A:

Q: (a) y" + 7y + 12y = 0, y(0) = -1, y(0) = 0 %3D %3D

A: We have to find general solution and it's sketch.

Q: 8: Which one of the following conics is a parabola? 22 + y + 5 = 4æ B 222 + y? = 4x +4 4r – 9y? +…

A:

Q: The points of intersection of the graphs of xy = 20 and x² + y? = 41 are joined to form a rectangle.…

A:

Q: Find the point P on the parabola y = x² closest to the point (57, 0). (x, y) = y y = x? P 57

A: Given that, the function y = x2 To find the closest point P to the point (57,0) Let (x, x2) be the…

Q: enclosed betw parabola y = x2

A:

Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A:

Q: . Find the point on the parabola y = x² closest to (6,3). newor: The noint is (24)

A: Given curve is y=x2

Q: Find the area of the largest rectangle with the lower base on the X-axis and the upper vertices on…

A:

Q: (b) Find the evolute of the parabola y? = 4ax.

A:

Q: Find the point P on the parabola y = x? closest to the point (57, 0). (x, V) = ( y y =x 57

A: Let x, x2 be the point on the parabola y=x2 closest to the point 57, 0. Now the distance between x,…

Q: 5.Find the point on the parabola x? = 4y nearest to (0,4).

A: Given:      x2 = 4y    Point : ( 0 , 4 )

Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

Q: 4. Fit a second degree parabola y = a + bx + cx? to the following data 2. 8. 10 y 3.07 12.85 31.47…

A:

Q: 10. Which equation represents the parabola that has been vertically stretched by a factor of 5,…

A:

Q: 1) y = ax2 ;What values of a will make the parabola open down? %3D

A:

Q: 16. Which equation represents the given parabola?

A: We want to find the equation of given parabola.

Q: Given the general form of a parabola x2+8x-28y+10=0, what is the y coordinate the vertex? k=_____.…

A: Given that the general form of a parabola is x2+8x-28y+10=0 . Here we have to find the y coordinate…

Q: of a, b, c, and d. 77. For what values of a and b is the line 2x + y = b tangent to the parabola y =…

A: Given curve is  We know that slope of tangent to curve y=f(x) at x=a is value of dy/dx at x=a…

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 6. 3. 3/4

A: Converting the equation to standard form

Q: A parabola is modeled with the equation x2 – 6x + 4y – 19 = 0. Which is the domain and range of the…

A:

Q: 3. The diagram shows a cuboid that is formed by bending a long wire of length 336 cm?. h 3x (a)…

A: Given:  The diagram shows a cuboid that is formed by bending a long wire of length 336 cm. To Find:…

Q: Find the coordinates of the vertex for the parabola. Round your answer to 2 decimal places. Include…

A: Given query is to find the vertex for the parabolo.

Q: Find a or k so that the points (-5,-8) and (1,-25) lie on the parabola y=a(x+3)²+k

A:

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: Solve the following problems. Show the complete solution. What is the equation of the line to the…

A: For tangent line first  find the slope of the line at that point ..then find the equation of line

Q: 3. What is the radius of the circle passing through the vertex and endpoints of the latus rectum of…

A:

Q: What is the equation of a parabola with vertex at the origin, and focus is on the x-axis that passes…

A:

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.