Use the parametric equations of an ellipse,x=6cosθ,y=4sinθ,0≤θ≤2πto find the area that it encloses. Area of an ellipse: We can calculate the area of an ellipse with the help of the semi-major axis and semi-min...
The parametric equations for the normal line are represented by x(t)=x0+fx(P)t, y(t)=y0+fy(P)t, z(t)=z0+fz(P)t. The line passing through the point with the normal vector of the gradient of the surface at the point is the parametric equation of the ...
The ellipse x^2+3y^2=13 , has two points when x=\pm 1 . Find the slope of the ellipse at both these points. Find the vertices and foci of the given ellipse. (x^2)/16 + (y^2)/64 = 1. Find an equation for the conic that satisfies the given conditions. Ellipse, foci (0,...
Find an appropriate parametrization for the given piecewise-smooth curve in R^3. The intersection of the plane z=3 with the elliptical cylinder \frac{x^2}{9}+\frac{y^2}{16}=1 Find parametric equations for the curve with the given properties. The ellipse: {x^2} / {a^2} +...
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Find parametric equations for the curve with the given properties. The ellipse: {x^2} / {a^2} + {y^2} / {b^2} = 1 Consider the parametric curve: x=15costheta, y=9sintheta, -pi 2 leq theta leq pi 2 . The curve is (part of) an ellip...
Consider the parametric curve: x = 10 cos theta, y = 6 sin theta, - pi/2 less than or equal to theta less than or equal to pi/2 The curve is (part of) an ellipse and the cartesian equation has...
Consider the paraboloidz=x2−y2. The plane9x−6y+z−3=0cuts the paraboloid, its intersection being a curve. Find the natural parametrization of the curve. Intersection of plane and a paraboloid The locus of points of ...
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