6. Find the parabola y = ax² + bx +c passing through the points (–2, –6), (1, 6), and (3, 4).

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  Vertex: (2/3 ,…

A:

Q: Identify the graph of the linear equation 4x + 2y + z = 8 in three dimensional space. (0,0,2) (0,…

A: We need to identify the graph of the function 4x+2y+z=8 We will do so by seeing if the points that…

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

A:

Q: Classify each conic section. 23) 2y + x + 8y + 11 = 0 24) x + y + 4 = 0 25) -x + 6x + y – 6 =0 26)…

A:

Q: Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9.…

A: As per guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

Q: Find a function whose graph is the lower half of the hyperboloid -x2 - y2 + z2 = 1.

A:

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

A:

Q: 7. A quadratic curve y= ax² +bx+c passes through the points (-1,4), (1,–5) and (3,5). Find the…

A: A quadratic curve is y=ax2+bx+c passes through -1, 4, 1, -5 and 3, 5To find the equation of the…

Q: Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y –…

A:

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

A:

Q: 3. Where do the asymptotes intersect for the hyperbola y = ( 2x +3 ) / ( 8x +5 ) O ( 3/8 , 2/5 ) O…

A: Given : Hyperbola y =2x + 38x + 5   To find the asymptotes.

Q: The vertex of the parabola f(z) = + 6z + 7 is O (-3,-2) O (-6,-18) O (-6, -2) O (-3,5) O (-9,-2)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: The vertices of the hyperbola y = 5+ ( x² + 9 )0.5 are Select one: O(0,-3) and (0,3) O(8,0) and (…

A:

Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: Show that the system of confocal and co-axial parabolas y²-4a(a+x) is self orthogonal, where a is…

A: If the two curves in the family cut each other at the right angle, then they are considered as self…

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: 8. Find a, b and c so that the parabola whose equation is y = ax² + bx + c has the vertex at (3,2)…

A: As we know that for the parabola y=ax2+bx+cthen its vertex is given by (-b2a,4ac-b24a)

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: 2. Show that ( 1, 6), (0, 3), (1, 2), and (2, 3) lie on a common parabola.Hint: For scratch work,…

A:

Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

A:

Q: What kind of conic section (or pair of straight lines) is given by the quadratic form Q(x1, x2) = x…

A:

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

A:

Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

A:

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: 9. Find an equation of the hyperbola whose transverse axis is horizontal, with center at (2, –2) and…

A:

Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

A: We have to determine the equation of the parabola whose vertex is at the point (-1,-1) and whose…

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. 2(x -…

A:

Q: Find the maximum and minimum values of f(x, y) = 7x + y on the ellipse x2 + 9y² = 1

A:

Q: Find b and c so that y = 7x2 + bx + c has vertex (– 6, 2). - С —

A:

Q: Find the smallest outputs of the function x^2+2y^2 on the slanted ellipse x^2+y^2+xy=3

A:

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)…

A: The quadratic function is given by fx = 2x-32+1 To evaluate : The vertex of the parabola defined by…

Q: Find the minimum and maximum values of f(x, y) = x2y on the ellipse 4x2 + 9y2 = 36.

A:

Q: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

A:

Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

A:

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = c. Sketch some of…

A:

Q: 9. Find an equation of the parabola that satisfies the given condition: Vertex V(-1,0) and focus…

A:

Q: 3- The parabola y= ax'+bx+c, mean that the cquation y = ax is .........

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: 3. Find the family of orthogonal trajectories of the family of ellipses centered at the origin and…

A:

Q: use the vortex (h,k) and a point on the graph (x,y) to find the general form of the equation of the…

A:

Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: 19 Find the minimum value of the parabola y = x – 8x +

A: The minimum value of the parabola or any curve is obtained where y' = 0