8-1) Assume that two surfaces to create a curve : 炉 x² + x²-x²3² = -7 are intersectiong 3x₁² + x₂ + x3 = 13 Determine the equation of the tangent to the curve at the point (1,1,5). line

Q: The distance between the line x - y + 3 = 0 and the line y = x + 2 is

A: The given two lines are x-y+3=0  and y=x+2. The equation of second line can be written as x-y+2=0.…

Q: The distance from the origin to the line passing through the points (0, 1,3) and (1,-1,2) is 14.

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Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t ,y=-2t+1 ,z=t is

A: We are supposed to find the distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t…

Q: Find the equation of the circle which is touched by y = x has on the positive direction of the x -…

A: Since the required circle has its center on the x-axis,let the coordinates of the center be…

Q: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

A:

Q: Compute the distance from the point (3, 0, -1) to the line containing the points (1,0,−4) and (1,…

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Q: Determine if the line 8x-y= 2 and the line containing the two points (1,3) and (2,-4) are parallel,…

A:

Q: For the curve y = ax + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: we have to solve the problem

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

A:

Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: (c) Find the slope of the curve x?y + xy? = 6 at the point (2, 1).

A: Slope of a curve is given as dy/dx. Pount given is (2,1)

Q: Find the points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: What is the distance between points (0,0) and (-3,4)?

A: Given points are  We know that distance between the points (x1,y1) and (x2,y2) can be calculated by…

Q: 1.) y = 2 X²+1

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

Q: Find the line perpendicular to y=2x-3 and through the point (2,-3) B) find the lines both parallel…

A:

Q: Let A be the point with coordinates (2, -1, 0) and let B be the point with coordinates (2, 0, 0).…

A: let A be the point with coordinates 2,-1,0 and let B be the point with coordinates 2,0,0 let l be…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: From the point (0, –5), tangent lines are drawn to the circle (x – 7)2 + y = 4. Find the slope of…

A: Equation of line passing through point (x1,y1) and slope m  (y-y1) = m (x-x1)

Q: Assume a line y = mx + c, [asses through the points (1, 15) and (-3, -5) Determine the slope, m, of…

A: