Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive parameter.

Q: find the radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

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 radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

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Q: Find the radius of curvature at any point on parabola y2=4ax

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Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: find a parametrization for the curve. the left half of the parabola y = x^2 + 2x

A: First, we will find the symmetric line of the given parabola y=x2+2x. We know that the symmetric…

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

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Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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Q: Find equations of both the tangent lines to the ellipse  x2 + 4y2 =36 that pass through the point…

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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: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: state whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: Rearrange the equation, 3x2-7y2=z by dividing both sides by 21 and obtain x27-y23=z21. The general…

Q: Find points P and Q on the parabola y = 1 – x² so that the triangle ABC formed by the x- axis and…

A: We have △ABC is an isosceles right angle triangle. So the interior angle at B and C must be 45° The…

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

Q: 7. Eliminate the parameter to find a Cartesian equation of the curve: x = Vt, y = 5 – 3t

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Q: Find the tangent to the ellipse x? + y² = 1 at P:(V2,1//2). %3D 4 ソ-Va z-Zol

A: Solution:-

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

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

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Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

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: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

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Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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Q: Find the least radius of curvature of the cubic parabola y=x3.

A: Given To find the radius of curvature, first find the curvature (K) using the formula. Find the…

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: 3x + xy? 2y + x?y dy dx

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Q: The points P(ap2 , 2ap) and Q(aq2 , 2aq) lie on the parabola y2= 4ax. Prove that if PQ is a focal…

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Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: Find the y coordinate of the center of curvature of the parabola at (2,2). 7. -7 -6 6.

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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: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

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

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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 an equation of the tangent plane to the given surface at the specified point. 2x2 + y? – 9y,…

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Q: Find the curvature of the parabola y = x² at the origin.

A: Given :-   parabola y=f(x) = x2  To find:-  curvature of parabola at origin(0,0)

Q: Let f(x, y) = x? + 4y. Find the extreme values of f on the ellipse x? + 2y? = 1.

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

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Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

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

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