Calculate the curvature of the ellipse x2a2+y2b2=1 at its vertices.

Q: Write the equation of Spheres with radius R.

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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 standard equation of the sphere with the given characteristics. Center: (-1, –3, 4) Radius:…

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: Show that the ellipse x = a cos t, y = b sin t, a 7 b 7 0, has its largest curvature on its major…

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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: Show that the parabola y = ax2, a ≠ 0, has its largest curvature at its vertex and has no minimum…

A: Using the relation,

Q: Prove that the parabola y = x^2 at the points where the line has an angle of inclination "o" the…

A: Curvature of  a graph y= f(x)  k=d2ydx21+dydx232

Q: Find the PARAMETRIC model that models the trajectory of the ball.

A: Solution  Given The exit velocity of baseball is 128 feet per second , in the direction of 30. above…

Q: Graph the surface whose spherical equation is p = 1– sino.

A: We use maple software to graph the given surface.

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –-2, 4)…

A: NOTE: Refresh your page if you can't see any equations. . the center is  and the radius is

Q: Find the standard equation of the sphere with center (-4, 3, 8) that is tangent to the plane given…

A: The center of the sphere is (-4,3,8) . The tangent plane is 3x+8y-4z=24 The radius of the sphere is…

Q: What is the relation of the conic section to the oblong plate?

A: Key Points A conic section (or simply conic) is a curve obtained as the intersection of the surface…

Q: Find the curvature of the ellipse with major axis's length (12) and minor axis (6) at the point…

A: The curvature K of a curve y=fx is given by, K=d2ydx21+dydx232⋯⋯1 where, f'x and f''x are the 1st…

Q: What are the parametric equations for an ellipse centered at the origin with a major axis of length…

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Q: What is the highest point on the ellipse that is the intersection of the plane x + y + 2z = 2 and…

A: Given  the intersection of the plane x+y+2z=2 and the paraboloid z=x2+y2

Q: Give some typical parametrizations for lines, circles, parabolas, ellipses, and hyperbolas. How…

A: The equation of the line is in the form of ax+by=c. The parametric equation for the lines are as,…

Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z=2 and the…

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Q: A searchlight is shaped like a paraboloid of revolution.If the light source is located 2 feet from…

A: draw the parabola used to form the searchlight on a rectangular coordinate system so that the vertex…

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

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Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

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Q: Find the curvature of the curve =.

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Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z = 2 and the…

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Q: At what point does the curve y = e have maximum curvature? What happens to the curvature as x → ∞?

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Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 + 2z2 −…

A: The quadric surface given to us is: x2+y2+2z2-2xy+4xz+4yz=16 This is compared to the general form of…

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

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, =7,2) Radius:…

A: Explanation of the answer is as follows

Q: Find the curvature of the ellipse x=4 y =5sin t at the points (4,0) & (0,5).

A: In this question we will use basic of calculus i.e concept curvature of ellipse. We will simply…

Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Calculate the curvature of the ellipse x2/a2+y2/b2=1

A: To determine the curvature of the ellipse.

Q: Give some typical parametrizations for lines, circles, parabolas, ellipses, and hyperbolas.

A: We have to find the parametric equation of the line, circle, parabola, ellipse, and hyperbola. (A)…

Q: Show that the parabola y = ax2, a  0, has its largest curvature at its vertex and has no minimum…

A:

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –3, 5) Radius:…

A: Given that: Centre of the sphere, (h,k,g)= (-1, -3, 5) and radius, R=6

Q: State the formula to find the Curvature of a curve in parametric form.

A: We will state the required formula.

Q: Calculate the curvature of the ellipse x2 / a2+y2/b2=1 at its vertices.

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Q: A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)

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Q: Find the curvature of the parabola f(x)= ax +bx+c at its vertex 2a ’

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

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: Find the curvature of the plane curve y = 4t³ at the point t = 2.

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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: Show that the ellipse x = a cos t, y = b sin t, a > b > 0, has its largest curvature on its…

A: Consider the given equation as x=acost, y=bsint and a>b>0

Q: Find the curvature of the curve ř= .

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Q: What is the radius of curvature at point (1, 2) of the curve 4x - y2 = 0.

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Q: Find the surface area of the ellipsoid obtained by rotating the ellipse (=) = 1 about the x-axis.

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Q: Show that the ellipse x = a cos t, y = b sin t, a> b>0, has its largest curvature on its major…

A: The curvature for a parametrized curve c(t) = x(t)i + y(t)j is :

Q: What are the coordinates of the highest point where the circular cylinder intersects the Elliptical…

A: We will use lagranges multiplier theorem to find heighest point

Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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Q: Find the curvature and radius of curvature of the curve y=cosmx at a maximum point.

A: Given curvey= cos mxWe have to find curvature and radius of curvature at maximum point .Formula…