Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written as det 1 = 0. 1 x2 Y2

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

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Q: The equation of the tangent line to the curve z +y = 25, at (4,-16) is 4 y%= %3D 16 16 (z - 4) + 16…

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Q: Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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Q: Find an equation of tangent equation is 2x+6y=3. line to the graph of y=x+lax that is perpendicular…

A: We need to find the equation of the tangent line to the graph y=x+ln(x) that is perpendicular to the…

Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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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: 5. Find the equation of the tangent and normal line of 2x+1 y = at point (1,1). x+2

A: A detailed solution is given below     (As per our guidelines, we have to solve only one question)

Q: What is the equation of line L passing through (-1,3) that is tangent to the curve…

A: Let's Solve, Answer : Option E

Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

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Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

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Q: Find the equation of the tangent line to the curve 3 x' + 2 y – 22 = 3 xy – x at the point (2, 2).…

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: The equation of the line is      x+2y-6=0⇒y=-12x+3       in the form of line equation y=mx+c  So,…

Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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

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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 all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: Verify that (4,1) on the curve x + /xy = 6 and find the lines that are tangent and normal to the…

A: Given that, the curve is x+xy=6. Differentiate the curve x+xy=6 with respect to x as follows,…

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Show that the curve of y = 2e2z + 3r + 2r3 has no tangent line with slope 2.

A: The given curve is y=2e2x+3x+2x3. Obtain first derivative as follows. dydx=ddx2e2x+3x+2x3=4e2x+3+6x2

Q: Compute y / x for the interval [2, 5], where y = 4x - 9. What is the slope of the tangent line at x…

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Q: 2х at (1,1) (x+1) Find the equation of the line tangent to y = a) x-2y =-1 b) 2x-у - 1 c) х-у -2 d)…

A: First I have written the formula of tangent line to a curve at given point, just use them for given…

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

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Q: Find equations of the tangent lines to the curve х — 1 x + 1 that are parallel to the line x – 2y =…

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Q: Find an equation of the line tangent to y = xsin x at the point x = 1.

A: The given equation is y=xsinx.

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

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Q: What is the equation of the line tangent to curve defined by x + 4y² = 17 at the point (1, -2)?…

A: equation of line tangent

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: Let (21, Y1) = (7,9), m = 3. Then the equation of the tangent line is O y = 3x- 20 O y = 3r - 16 O y…

A: Equation of the tangent line = ?

Q: Find the equation of the tangent line to the curve y = 2 In(x - 26) at the point (3,0). %3D y =

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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: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: At what point on the curve y = 4 + 2e* – 4x is the tangent line parallel to the line 4x – y = 5? (x,…

A: Given: y=4+2ex-4x   and 4x-y=5

Q: 7. What is the equation of the tangent line and the normal line to y = x² – 4x + 2 at (4,2)…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Find the equation of a tangent line to the curve y= 2x3 - 3x² - 10x + 1 which is perpendicular to…

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Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

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 point of intersection of the tangent line to y=sin( 2x) at y=0 and the line r+2y 5. O (5,0)…

A: let us first ind the equation of tangent  line

Q: 2. Find the equation of the line that is tangent to the curve y 3 + 3y = x 2 at the point (2, 1).

A: Find the equation of the line that is tangent to the curve y3 + 3y = x2 at the point (2,1).

Q: Find the equation of the line tangent to the curve 2(z² + y°)* = 25(z² – y²) at the point (3, 1).…

A: Suppose a line passing through with slope  m then equation of line is .