tangent to the parabola y=x^2

Q: Find parametric equations for the normal line to the surfacez=-7x2 -9y2   at the point  (2,1,-37)

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Q: A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on this…

A: We answer only one question at a time , so we will answer the first question since the exact one…

Q: Line L is perpendicular to the line 6z – y = 7 and passes through the point (0, 6). Line M is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (4,). %3D

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Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 208 feet.…

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Q: In a flat geographic region, the course of two rivers can be represented approximately by the…

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Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: What are the new coordinates of the point (11, 22) under the dilation (x, y) → (2x, 2y)?

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Q: The length and diameter of a spaceship as  determined by an astronaut on board are 76m and 23…

A: The length and diameter of a spaceship as  determined by an astronaut on board are 76m and 23 m,…

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: The general equation for a parabola is given as, y=kx2 Let the x-axis represents the road surface…

Q: Find the points where the line y=x4 intersects a circle of radius 2 centered at the origin. Give…

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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: Find the points where the line y=−3xy=-3x intersects a circle of radius 2 centered at the origin.…

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Q: A frameless painting with a size of 2 meters by 2 meters hangs on the side of a wall where its…

A: Solution of the problem as follows

Q: Find the parametric equations of a line through point 4 (4,-9) and slope 3 -

A: detailed solution is given below

Q: If the straight lines are coplaner then they are?

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Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: Find the number of points in the xy-plane with integer coordinates located at a distance 5 from the…

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Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: What are the new coordinates of the point (6, 15) under the dilation (x,y) → (3-3)?

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Q: Find the slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: A line, passing through point (6, 3, 2) and is perpendicular to the xy-plane. Find a point on this…

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Q: What is the equation of family of central conics with common foci and axis. Determine its orthogonal…

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Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: What are the parametric equations for the line segment from (3,2) to (-10,5)?

A: To determine the parametric equation of a line segment.

Q: The line through the origin whose projection on the xy-plane is a line of slope 3 and whose…

A: In this type of questions we assume a line an points on that line. Suppose we have a line and points…

Q: A point moves such that the ratio of its distances from two fixed point is constant, show that its…

A: Let the moving point be P (x, y, z). Let A(a, 0, 0) and B(-a, 0, 0) be two fixed points.

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Find the points where the line y=−x/4 intersects a circle of radius 8 centered at the origin. Give…

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Q: There are two points on the x-axis that are located a distance of 6 units from the point (3, 1).…

A: Let the coordinates of the two points on x-axis be: (a, 0) and (b, 0). These two points are…

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 136 meters.…

A:

Q: The drone starts at point (0, 0), the landing pad is at point (11, 3) and the parabolic path must…

A: Given

Q: How to determine is a mountain of certain height is visible from a distance of 65 miles if line of…

A: Given:  h           = Mountain height  65miles = base distance θ          = angle of line of…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: When a figure is dilated and the segments pass through the center of dilation, the pre-image will be…

A: Here, we have given that a figure is dilated and the segments pass through the center of dilation.

Q: There is a line through the origin that divides the region bounded by the parabola y=7x-(2(x)^2) and…

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Q: Find an equation for the line tangent (in general form) to the circle at point (4,-3). The circle…

A: For the figure  given below: Equation of a tangent to a circle at point (a,b)  with radius r and…

Q: A parabola is the set of all points in the plane that areequidistant from a fixed point called the…

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Q: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

Q: A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the…

A: Introduction :

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

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Q: A line with the slope of 1/(1/2) passing through the origin will intersect the rectangular region.…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the…

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Q: Find the length of the arc of the curve 9y2 = 4x³ from the origin to the point (4, ). %3D

A:

Q: A suspension bridge with weight uniformily distributed along its length has twin towers that extend…

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.