A parabola is opening downward, always having a length of latus rectum equal to 4. The vertex of this parabola always exists at the line x = 2. An orthogonal trajectory intersects this parabola at the y - intercept of 1. The vertical asymptote of this orthogonal trajectory to the parabola is located at x = If decimals, use 8 decimal places.

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

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A: Known facts: The average value of minimum and maximum of the sine or cosine graph is called vertical…

Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

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Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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A: Explanation: Given that,                     Assume that, point of tangency is (a, a2). Slope of…

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A: The given equation of ellipse is,

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A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

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A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: Find the equation of the hyper bola with latus rectum 1, slope of asymptotes +- 1/2. Draw the curve.

A: Consider the general form of the hyperbola is, x2a2-y2b2=1 Since, the latus rectum is 1 then,…

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A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

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A: Given ------(1)   The average value of a functionon an interval is given by ------ (2) From the…

Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

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Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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Q: If PP' is a diameter of the rectangular hyperbola xy = c' show that the locus of the intersection of…

A: given , if PP' IS a diameter of the rectangle hyperbola xy = c^2  show that the locus of the…

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

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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: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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A: Equation of tangent problem.....

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Q: Find the coordinates of the point at -50° on a circle of radius 4.7 centered at the origin.

A: x=r cos θ , y=r sin θr is the radius, θ=-50°

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Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Find the length of the tangent to the circle x²+y²-2x-3y-1=0 from the point (2,5).

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Q: 11. Show that the tangent to the hyperbola x-y = 1 at the point P(coshu, sinhu) except when vertical…

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Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the…

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the…

Q: A parabola Is opening downward, always having a length of latus rectum equal to 4. The vertex of…

A: vertical assymptotes are vertical lines ( parallel to y-axis ) which touches the curve at infinity…

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Q: At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time?…

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

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

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Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

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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: The slope of the tangent line to the parabola y=2x^2+2x+7 at the point where x=4 is: slope =…

A: The equation of the parabola is y=2x2+2x+7

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x – 5), (9, -1)…

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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: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: Find the orthogonal trajectories of the family of parabola described by the equation (x+2} = cy.…

A: Explanation of the answer is as follows

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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