1. Sketch the graph for a parabola with AOS at x = -3, minimum of 2, and an y-intercept at 5. Label your graph! (y-int, vertex, AOS, y-intercept reflection point)

Q: b) Draw the parabola with a minimum value of -8, zeros at 2 and -2 and y – intercept of -8.

A: Answer

Q: Find the family of curve that intersects the family of hyperbolas y² = 2x² +b at an angle arctan(1).

A: To find the family of the curve that intersects the family of hyperbolas y2=2x2+b at an angle…

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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

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Q: 2)Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the…

A: Given the flashlight is shaped like a paraboloid and the light source is placed at the focus so that…

Q: A rectangle is to be inscribed inside a semi-ellipse + = 1, -2 <IS2 and 0 y S 3. Give a rough sketch…

A: Solution is here

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the…

A: Given: f(y)=y2(9−y2)  To find: Solution

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

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: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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Q: If a parabola has a minimum at the point (-2, 4), the parabola has... O one positive x-intercept,…

A: The vertex form of a parabola is defined by the equation, . If a parabola faces up, it has the…

Q: 5. What is the standard for equation of a parabola with its vertex at (0,0) and a directrix of x-3?…

A: Given: A parabola has vertex 0, 0 and directrix x=3      ……1   To find: Equation of parabola

Q: The line y = mx +b intersects the parabola y = x^2 at points A and B. Find the coordinates of the…

A: The line y=mx+b intersects the parabola y=x2 at the pointsA and B.Let A=x1,x12 and B=x2,x22, where…

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

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: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: Find the standard form equation for a hyperbola with vertices at (0, 3) and (0, – 3) and asymptote y…

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Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

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: What is the minimum vertical distance between the parabola y =x2 +1and y =x -x2 ?

A: Given:

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: Ellipses

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 –…

A: first we have to draw the sketch of y = 1-x2 and draw a rectangle beneath it From the graph we can…

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: Find the equation of the hyperbola that is centered at (0,0), has vertices at (t10,0) and has 6.…

A: Consider the given values. Center=0,0vertices=±10,0y=±65x The gerneral equation of hyperbola with…

Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

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Q: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

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: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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Q: 4. What is the family of curves for all parabolas with axes parallel to the y-axis. Add File

A: We will find out the required solution.

Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: 1. Which of the following best describes the graph of y = x? – 4x + 2? a parabola with a vertex at…

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Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

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Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: 10. Draw the parabola with the following conditions a) A zero at (1, 0) the vertex at (3, -4) and y…

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Q: Determine the family of curves of all parabola's with axis parallel to the x-axis and with distance…

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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

Q: 11. Show that the tangent to the hyperbola x- y = 1 at the pomt P(coshu, sinhu), cuts the x-axis at…

A: We will be using the definition of tangent line to solve the problem

Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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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.