a. Show that the points (2, 9), (−1, −6), and (−4, −3) are not collinear by finding the slope between (2, 9) and (−1, −6), and the slope between (2, 9) and (−4, −3). b. Find an equation of the form y = ax2 + bx + c that defines the parabola through the points. c. Use a graphing utility to verify that the graph of the equation in part (b) passes through the given points.

Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the…

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.

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: Find the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

Q: For the parabola y2 = 4ax, the line segment joining the two points (a, 2a) and (a, - 2a) is called…

A:

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

A:

Q: How can we find the slope of the parabola y?

A: You can’t find the slope of the parabola y , because a parabola is not a line. You can find the…

Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

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

A:

Q: Determine the value of p (where |p| corresponds to the distance from the vertex to the focus) of the…

A: Given: Parabola whose vertex is 6, 7 and the x-intercepts are 3, 0 and 9, 0. To determine: Value of…

Q: Find an equation for the parabola that has a horizontal axis and passes through the given…

A:

Q: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

A:

Q: A parabola has an equation of x2 = 6y + 10. Determine the equation of a diameter of the parabola…

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

Q: 5. If graphed, which of the following parabolas would lie entirely below the x-axis? (1) y=x² +5x+10…

A: We’ll answer the first question  . Please submit a new question specifying the one you’d like…

Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

A:

Q: Find an equation for the parabola that has its vertex at (1, 2) and its focus at (4, 2).

A: The vertex of the parabola is the point of intersection parabola with its axis. The general form of…

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: Find an equation of the parabola that satisfies the given conditions.Vertex at the origin, symmetric…

A: Since the parabola is symmetric to the y-axis and has vertex at the origin, The equation of the…

Q: Find an equation of the line containing the centers of the two circles               x2 + y2 - 4x +…

A: The given equations are x2+y2-4x+6y+4=0    and   x2+y2+6x+4y+9=0. Rewrite the above equations in…

Q: Given a parabola with vertex at (8,-4) and focus at (-4,-4), determine the equation of the parabola.…

A:

Q: Which of the following equations is the equation of tangent to the parabola   y2 = 2x + 8   at…

A:

Q: Find an equation of the line containing the centers of the two circles x2 + y2 + 2x + 2y + 1 = 0 and…

A: Given,

Q: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

A:

Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

A:

Q: Find an equation of the parabola that satisfies the given conditions.Vertex V(3, -2), axis parallel…

A: GivenV(3,-2)y-intercept -1To  find  equation of parabola.

Q: Find the length of the diameter of the ellipse 3x2+y2 +2x-6y=0. Which has a slope of 2.

A: Ellipse

Q: Graph the curves and show that the 2x2-y2=C is a solution to yy'-2x=0.

A:

Q: ^2+84x-24y

A: Given Ellipse: 21x2-4y2+84x-24y=36This equation can be re-written as-21(x2+4x)-4(y2+6y)=36 To find…

Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

Q: =r such that the point (2, 1) is on the segment AB and the midpoint of Determine the coordinates of…

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Q: Find the point(s) of intersection of the parabolas y =x2 andy = -x2+ 8x.

A: Definition used-      Point of intersection-           For finding the point of intersection of…

Q: If the parabola whose equation is x = ay2 + by + c has its vertex at (3,2) and a> 0, then it has…

A: The given statement is that" if a parabola whose equation is x=ay2+by+c has its vertex at 3,2 then…

Q: Find the equation of the line containing the point  P(−1, 3)  and perpendicular to the graph of…

A: To find the equation of the line containing the point P(-1,3) and perpendicular to 3x+6y=-1

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

A:

Q: Find all the values of b such that the parabola y=(1)/(8)x^(2)-bx+(9)/(2) will have a directrix…

A: the given equation of the parabola is y=18x2-bx+92. we have to find all the values of b so that the…

Q: 1. Describe an algebraic method for determining the x-intercepts, if any, of a parabola which…

A:

Q: The directrix of the parabola x2 – 4 y = 0 is

A: According to our guidelines we are supposed to do only one question . Kindly repost the other…

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

A:

Q: Find an equation for the parabola that has its vertex at the origin and has a directric at x=1/29

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

Q: Find an equation for the indicated half of the parabola.Upper half of (y - 2)2 = x - 4

A: Given: y-22=x-4 For finding equation of the upper half of the parabola, we take square root both…

Q: Find the standard form of the equation of the parabola that has a vertex at (1,-3) and passes…

A:

Q: The coordinates of the turning point of the parabola whose equation is y = x – 6x + 8 are A (3,35) ©…

A: Given,  Equation of parabola: y= x2 - 6x + 8 We need to determine the coordinate of turning point…

Q: Find a, b, and c so that the graph of the parabola with equation y=a+bx+cx^2 passes through the…

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.