Find the line through (1,-1,1)and normal to the line  3x=2y=z , and parallel to the plance  x+y-z=0 .

Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: What are the equation of line passing through (-1,3) that is tangent to the curve x^2 + 4y^2 – 4x –…

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: of intersection(s) of the normal line to the curve y=((9x^3)/(8x+4)) wherein the slope of the curve…

A: Given: The curve equation is The line equation is  2x+y=0

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0…

Q: Pls help ASAP

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Q: Verify that (2,3) is on the curve x²+xy-y²=1 and a. find the line that is tangent to the curve at…

A: Given curve, x^2+xy-y^2=1

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

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Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: Solve the center qnd radius of the circle passing through the points P(1,1) and is tangent to the…

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Q: The antiderivative of a constant is the family of lines.

A: Let y = mwhere m = constant

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. 4x² + 9y =…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find the equations of the normal line to the surface z = at the point (1, - 2, 32). - t + 32 ||

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Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 2. What is the slope of the line tangent to the curve 8x³ – y² = 4 at the point (1,-2)? 3. What is…

A: Since first subparts question statement missed. Answer 2 and 3

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

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Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is perpendicular to the…

A: Given: The curve is y = 2x3 - 3x2 - 12x + 20 and the tangent line is perpendicular to the line y =…

Q: Find the equation of the normal line at the point indicated. y= 3x^2-2x+1 at (1,2

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Q: b) Find equation of line passing the point ( 4, -1) and normal to 3y+ x=1. ||

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Q: Find an equation of the normal line to the parabola y = x 2 - 5 x + 4 that is parallel to the line…

A: Given:       y=x2-5x+4 is parallel to the line x-3y=5.

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A: To find the points at which tangent line is horizontal , y' =0.

Q: Determine the equation of the normal line to the curve y= 2 − (1/3) x2 that is parallel to the line…

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Q: Find the equations of the tangent and the normal lines to the curve x5 + y5 = 4 x2y2 at the point…

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Q: Find the equations of the normal line to the surface z = 2x°y* at the point (2, 2, 256). y = 2 = -t…

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Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal…

A: [Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: What is the image of the horizontal line through the point in under e ?

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Q: Find the equations of the tangent and the normal at the point indicated. y = x2 - 2x at its…

A: Given that - y = x2 - 2x at its points of intersections with the line y = 3

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Now when x = 3, we get Therefore the point (3, -4) is on the given curve. a). Slope of the tangent…

Q: Find the equation of a line normal to the curve x^2=16y at (4,2).

A: Solve the given problem.

Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: Find the equation of the line that is normal to the curve (y-x)2 = 2x + 4 at (6,2). %3D

A: Use equation of normal line

Q: What is equation of the line normal to graph of y = x^3 + 3x^2 + 7x - 1 at the point where x = -1? O…

A: Solving the problem by finding the normal of the given equation.

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &…

Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find the length of curve along y = x² from (0,0) into (2,4).

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.