A parabola is defined as being the locus of points P(x, y) that satisfy FP= MP, given coordinates F(5, 0) and where MP is the perpendicular distance from the point P(x, y) to the line with equation x =-5. The parabola has equation: A y = 20x B y = 5x y= 20x² D x² = 20y E y? = 4x

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

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: What is the equations of the tangent line in the given plane 1. Tangent to the parabola z = x^2 +…

A: The given surface is:…

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Tangent line equation problem....

Q: Find the minimum distance from the point (2, 4, 10) to the paraboloid given by the equation z = x +…

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Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: 1. Let P(1, yı) be a point on the parabola r = 4py, p> 0, with focus F(0, p). Let a be the angle…

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Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

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

Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

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

A: See the attachment

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: Find the tangent lines as directed. To the parabola y=6x-3 perpendicular to the line x+3y=7

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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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Q: Minimum distance between the parabolas y² – 4x –8y + 40 = 0 and x² –8x –4y + 40 = 0 is (A) 0 (B) 3…

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Q: The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation…

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Q: The plane x = 1 intersects the paraboloid z = x2 + y2 in a parabola. Find the slope of the tangent…

A: Given that the plane x = 1 intersects the parabolic z = x^2 + y^2 in a parabola.   So,…

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

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Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

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Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: (a) Find the first order DE corresponding to the family of parabolas y = Cx² . (b) Find the equation…

A: a)The family of the curve of the parabola is y=Cx2 To find the first order differential equation…

Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: Given f(x, y) = x² – 4y, the parabola x - 4y = 8 = 0 is the level curve o -8 None of the given…

A: The solution is given below

Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: Find the orthogonal trajectories of the family of parabola described by the equation (y – 3) = = cx…

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Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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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: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

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: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: 1 Let P be the parabola with equation y Lx2, L be the line with equation y = V3 7. 3 1 and M be the…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: 1. Let P(x1, Y1) be a point on the parabola x?: be the angle between the parabola and the line…

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Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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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: On a separate piece of paper, sketch the graph of the parabola f(T)= x+ 8. On the same set of axes,…

A: The equation of parabola is fx=x2+8 The coordinate of the point from which the tangents are drawn on…

Q: A y=1 x=y² B y=x² C (11) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and…

A: Given: Three regions A, B and C defined as: where region A is bounded by the parabola x=y2 and the…

Q: A parabola has an equation of x² = 6y + 10. Compute the equation of a tangent to the curve which has…

A: Given that a parabola has an equation x2=6y+10. Here we have to compute the equation of a tangent to…

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

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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Q: 16. Evaluate (x + V9) ds where C consists of two segments: the part of the parabola y = x² from…

A: In the given question we have to evaluate the integral ∫C(x+y)ds where C is the regionconsist of two…