Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2 and x^2 + z^2 = 9, where x ≥ 0
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y = x^2 − 3z^2 and x^2 + z^2 = 9, where x ≥ 0.
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- Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x atP(2, −1, −3). Express your answer in the form z = ax + by + c.Find the parametrization for the curve the lower half of the curve x+3=y^2
- Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2 at the point P(2, 1, -1), and show that the planes you find are perpendicular to each other.Find the equation of the plane tangent to the surface z = 10 − x^2 − y^2 at the point P0(2,2,2).List all of the points (x,y) on the parametric curve x=t^3+4t, y=6t^2 where the tangent line is parallel to the line with parametric equations x=−7t, y=12t−5.
- Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 ).Write the parametric equations for the tangent line to the curve of intersection of surfaces x=10x^2+2y^2 and z=x+y+10 at the point (1,1,12)Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and the cylinder of radius 3 wrapped around the y-axis.