Find the equation of the tangent plane to the given surface at the specified point   2x=y^2+z^2-9 at point (-2,2,1)   a) x=-2-2t, y=4+2t, z=2+t b) x=-2-2t, y=2+4t, z=1+2t c) -x+2y+z-7=0 d) x+2y-z+7=0

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: et C be the curve of the intersection of the two surfaces a² +} = z and 4x2 +y} +? =9. nd let L be…

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Q: A particle travels in the xy -plane with a path defined by the parametric equations x(t) = t - 3 and…

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Q: Consider the Folowing equation of a quadric surface 4×^2+9y^2+9z^2=36 a. Find the intercepts with…

A: Given question is Consider the following equation of a quadratic surface4×^2+9y^2+9z^2=36. We have…

Q: Find the equations of the tangents to the circle x^2 + y^2 + 4x - 10y + 21 = 0 that They are…

A: Find the equations of the tangents to the circle x^2 + y^2 + 4x - 10y + 21 = 0 thatThey are parallel…

Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2…

A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

Q: A variable straight line is drawn through the point of intersectio straight lines x / a+y/b = 1 and…

A: Given lines arexa+yb=1               ....(1)and  xb+ya=1               ....(2)Solving (i)and(ii) we…

Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: - The surface 5x^2 + 2z^2 = 3y is heading towards which axis? - Identify the surface generated by…

A: 5x^2 + 2z^2 = 3y x= 3n1 ,  y = -3(5n12 + 2n22) , z = 3n2

Q: What is the equation of the plane passing through the point (2, -3, 1) and perpendicular to the line…

A: A plane is a two-dimensional flat surface that extends indefinitely in all directions. It is…

Q: An equation of the straight line normal to surface x2 - y3 + z = 8 at the point P(2, -1, 3) on the…

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Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: the midpoint of line segment with end points (-1,6,2) and (3, 2, -4) What is the distance between B…

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Q: In two-dimensional Euclidean space, consider a curve defined by the equation x^2 + y^2 - 6x + 4y -…

A: In this question, we are provided with a quadratic equation in two variables x and y. In a…

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: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

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