Find the equation of the osculating plane at a general point on the cubic curve given by'r = (1, 2², 2³) and show that the osculating planes at any three points of the curve meet at a point lying in the plane determined by these three points.

Q: Find an equation of the line tangent to the intersection of the cylinders x² +2²= 4, y²2 +2²=4 and…

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Q: Find the coordinates of a rectangle with corner points at A: (2,4), B:(2,8), C: (5,8), and D: (5,4),…

A: We have to find co-ordinate after translating 6 units up and 2 units left

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: Find the parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

A: The parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

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Q: Point ZZ is located at (-5,-3)(−5,−3) on the coordinate plane. Point ZZ is reflected over the…

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Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: Find the parametric and symmetric equations for the line passing through the point P(1,-3,6) and it…

A: Equation of the line passing through the one  point and parallel to the given line

Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: ind point P and Q on the parabola y=(-x^2)+1 so that the triangle ABC formed by the x-axis and the…

A: Given that the curve is                         To find point P and Q on the given parabola, so that…

Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…

Q: The curve in the plane defined by the equation (*) (x^2 + xy + y^2 = 7) is a rotated ellipse, shown…

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Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: determine the parametric equations of the tangent axis to the ellipse x²/9+y²/4=1 at the point T =…

A: As we know that the parametric equation of ellipse at a point acosθ,bsinθ  is given by…