Consider measurements at points (0, 0), (1,8), (3, 8), (4, 20). 1. Find the best fit of a line C+ Dt for this data and sketch this line with the data. 2. Find the best fit of a constant line C for this data and sketch this line with the data. How do you interpret the result?

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

A: To find the condition of line ax + by = 1 which is normal to the curve a^(n-1) y = x^n

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

A: Given

Q: 5. Find the equation of the tangent and normal lines to the curve x = t2 – 2t, y= t3 - 3 when t =…

A: Firstly we find Slope of tangent and slope of normal to the given curves and then we will find…

Q: Find an equation of the normal line to the curve  y = x  that is parallel to the line  4x + y = 1.

A:

Q: 1. Find the equations of tangent and normal lines to the curve whose equation y? – 6x? + 4y + 19 = 0…

A:

Q: Find an equation of the normal line to the curve y = vx-3 which is parallel to the line 6x + 3y-4 0.

A:

Q: The equation of the tangent line to the curke x? + y = 36, at (6,-16) is %3D y = (x+6) + 16 16 16 16…

A: we have to find the equation of the tangent line to the given curve at (6, -16)

Q: (5) Find the equations of the normal and tangent lines to the curve at the point (1,2). y= =19x+59…

A: Differentiate both sides w.r.t. x.

Q: 1. Find the equations of tangent and normal lines to the curve whose equation y? – 6x² + 4y + 19 = 0…

A:

Q: Find the equations of the tangent and normal lines to the curve y=x²-2x-3 that is parallel to the…

A: The given equation of the curve {parabola} is y=x²-2x-3  and the given equation of the straight line…

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

A: Let y = mwhere m = constant

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

A: Given curve is The point (-1,3) lies on the curve if it satisfies the equation of curve Therefore,…

Q: Find the equation of the normal line to the curve x3+y2+2x−6=0 at the point (−1,3).

A:

Q: Q.3 a).Find equations of the tangent line and normal line to the curve y =x} - x+ 2 at the point (1,…

A: First find slope at given point then use equation of line

Q: Find the equations of tangent and normal lines of the curves at given points:  2?3 + 2?3-9xy=0 at…

A: To find: The equation of tangent and normal lines of the curves at given points. Given: The equation…

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

A:

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

A:

Q: Find an equation of normal line to the curve y = Vx that is parallel to the line 2x+y = 4.

A:

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: What is the point on the curve at which the normal line is parallel to the line Y = - 3X + 6? (The…

A: The function is given by y = 2x+1 The equation of the line is y = -3x+6 To evaluate: The point on…

Q: 4. What is the equation of the normal line to the curve 4x2 – 9y2 = 1 at point (3,2) ? a. y =x- 4 5.…

A: Slope of the Normal Line to the graph of f(x) is  -1f'(x). Equation of the line : y-y1=mx-x1 where,…

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

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

A:

Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find equations of the following. y = x2 − z2,    (6, 11, 5) find the tangent plane and normal line.

A: According to the given information: Consider the given equation at the given point:

Q: 9.Reduce the general equation of the given straight line y-x 3=4 to the normal form.

A: y-x3 = 4for normal form equation should be in the form x cosα +y sinα = p∴-x3 +y = 4

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

A:

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: Find the equation of the tangent line and the normal line of the curves at given point 1. 4x? + 9x?…

A: The given equation,     4x2+9x2=25, 2,-1

Q: find equation for the lines that are tangent andnormal to the curve at the given point.x^3/2 +…

A: Given: x32+2y32=17    at the point (1,4)

Q: 4. Find the equation/s of the normal line of slope 2 to the ellipse x² + 2y² = 3. 5. At what point…

A:

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

A:

Q: Find an equation of each normal line to the curve y = x³ – 3x that is parallel to the line 2x + 18y…

A: Solve the above question.

Q: The equation of the line tangent to the curve at (−1,4)is x+y=3. What is the slope of the normal…

A: Product of slopes of two perpendicular lines is -1.

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

A: follow next step

Q: Find an equation of the normal line to the curve y = x1/2 that is parallel to the line 2x + y = 1.

A: To determine a normal to the curve which is parallel to the given line

Q: (a) The temperature of a 22 m long metal bar is 14°C at one end and 33°C at the other end. Assuming…

A:

Q: Find the equation of the normal lines to the curve y=x^3-2x+1 that is perpendicular to the line…

A: Consider the given equation of the curve as y=x3-2x+1. Differentiate with respect to x we get as…

Q: Find the equation of the Normal Line to the curve y 2 = x at (4, 2). A 4х — у — 18 %3D 0 B 4х + у 18…

A:

Q: Find the equation of the tangent and normal line using the stipulated conditions   2.) x2 + 2y2 =…

A: The equation of tangent line is x2+2y2=9⇒x29+y292=1we have a=3 and b=92Since, we know that the…

Q: Find the equations of the tangent and normal lines x^2 + 2y^2 = 9 TL I to the line x + 3y = 7

A:

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 the equation of the tangent line and the normal line of the curves at given point 1. x? + y? -…

A:

Q: Find the equation of the Normal Line to the curve y² = X at (4, 2)

A: Given that,Equation of the curve is y2=x We need to find the equation of the normal line to the…

Q: 3. In Eercises, verify that the given point is on the curve and find the lines that are Haltangent…

A:

Q: Find the equation of the normal line to the curve y = 3x^2 – 2x + 1 at P(1, 2).

A: Topic = Application of Derivative