A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the %3D ratio 1: 2 is

Q: ...***... .. . .. The area of an ellipse with axes of length 2a and 2b is nab. The percent change in…

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

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

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Q: A sealed-beam headlight is in the shape of a paraboloid of revolution (parabolic shaped). The bulb,…

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Q: 5. If the receiver is placed at the focus of the satelite dish shaped like a paraboloid which has a…

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Q: find the equation of hyperbola with center (4,-1), transverse axis parallel to the y axis distance…

A: Given: A hyperbola with center 4, -1 , whose transverse axis is parallel to the y-axis. The…

Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

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

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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: 8. Determine the Equation of the Hyperbola if the Transverse Axis is 8 and the Foci are at (0, ±6)

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Q: Write the equation for the hyperbola with foci (1,-5), (9.-5) and conjugate axis of length 6. (x-…

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Q: 2. The points where a hyperbola intersects the line through the foci are called the

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Q: Find an equation of the hyperbola that has foci at (-15, 0) and (15, 0), and asymptotes y= x and y=

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Q: center, horizontally, is the car when it is at an altituue Ul 23 IL! 2. A truck has to pass under an…

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

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Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: On a separate piece of paper, sketch the graph of the parabola y = x² + 9. On the same graph, plot…

A: Sketch the figure.

Q: A parabola has its axis parallel to the x-axis, one end of its latus rectum at (-15/4,3/2) and…

A: Given Information:A parabola has axis parallel to the x-axis.Latus rectum at -154 , 32Vertex at (-1,…

Q: 17. Parabolas with axis parallel to the x-axis and with distance from vertex to focus fixed as a. Am…

A: This question is about family of parabolas.

Q: 6. There equations. are two line through (-2,0) tangent to the parabola y = 4r. Find their

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Q: Find the equation of parabola with rertex at (0,0 and focus at (3

A: Given the vertex is at(0,0) and focus (3, 0)

Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

Q: satellite dish shaped like a paraboloid, has a diameter 2.4ft and depth 0.9ft. If the receiver is…

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Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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Q: .... .. ......... ....*.*. ..* * ..... The area of an ellipse with axes of length 2a and 2b is nab.…

A: As per our guidelines , we can only solve first question. Please resubmit other questions as next…

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

A: The equation of directrix of the parabola is x+1=0. The length of the latus rectum is 3. The…

Q: 5. Find the equation of the hyperbola whose asymptotes are the straight lines x = 0 and y = 0 and…

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Q: 1. A parabola with directrix y = -1 and one endpoint of the latus rectum at (-1,3)

A: As per our guidelines we can answer only one question. please repost other seperately.  First of all…

Q: Find an equation of the hyperbola that has foci at (-2, 0) and (2, 0), and asymptotes y = x and…

A: The hyperbola has foci at -2,0 and 2,0 and asymptotes y=x and y=-x

Q: Find the equation of the hyperbola whose center is at point (4,−1), transverse axis parallel to…

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Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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Q: The area of an ellipse with axes of length 2a and 2b is A-πab. Approximate the percent change in the…

A: It is given that, the area of the ellipse with axes length 2a and 2b is

Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

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Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

A: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

Q: A parabola with directrix y = -1 and one endpoint of the latus rectum at (-1,3)

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Q: Find the length of the latus rectum of the parabola x2 = 4py. Then find the length of the parabolic…

A: Given , Equation of parabola  x2 = 4py     Comparing with the Standard Equation of Parabola  x2=4ay…

Q: A certain bridge arch is in the shape of the top half pf an ellipse 122 feet wide and 25.6 feet…

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Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: Find the length of the arc of the parabola x² 4ay measured from the vertex to one extremity %3D of…

A: We can calculate the length of arc using given condition and  formula of length of arc

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through from the hoop is modeled by the parabola,

Q: Determine the eccentricity of a hyperbola with a horizontal transverse axis of length 24 units and…

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Q: A satellite dish is shaped like a paraboloid, with the receiver placed at the focus. It is to have a…

A: The base of the dish is the vertex of the parabola. The parabola is upward oriented. Let the vertex…

Q: Which is the corresponding equation of the hyperbola with foci located at (−8, 0) and (8, 0) and a…

A: Given data is : Foci are -8,0 and 8,0 The transverse axis is 14 unit

Q: Find the equation of ellipse referred to its major and minor axes as the coordinate axes x, y…

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Q: What will be the equation of hyperbola that satisfies the given condition foci at (+ 24,0) and the…

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: Given that a person shoots a basketball overhand from a position 8 feet above the​floor, then the…