x3 = 3(y – 1) x(3y – 29) = 3

Q: If f(z) 2x2 2x + 3, find f'(-1). %3D 2a2 2x + 3 at the point (- 1, 7) Use this to find the equation…

A: We are given the function f(x)=2x2-2x+3. Now,           f'(x)=2x2-2x+3'       =2x2' -2x' +3'…

Q: (a) Prove that any two distinct tangent lines to a parabola intersect. (b) Demonstrate the result of…

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Q: f(x)=2x^2-7x+2 Compute f '(2) =?   Then Use this to find the equation of the tangent line to the…

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Q: 7-18 - Find the exact length of the curve. 7. y = 1 + 6x³/², 0 < x < 1

A: We find y' using the power rule

Q: Q1 (a) Solve the equation u + 2xy²u, = 0. Sketch some of the characteristic curves.

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Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: Sz(t) = - 2t2 ly(t)…

A: The objective is to to eliminate the parameter t to find a cartesian equation

Q: An equation of the line tangent to the graph of f(x) = x(1-2x)3 at the point (1,-1) is A. y = -7x+ 6…

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Q: a) [ i) Find the exact length of the curve y = x³ + 12x 1≤x≤2

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Q: the equation of the tangent line to the parabola at the given point.

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Q: The cartesian equation of the curve x = 1-t,y= t is : (a)y = 1– x², x20 (b)y =1-x ,x 2 0 (c) x = 1 –…

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Q: 4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the…

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Q: 1. Let P(1, yı) be a point on the parabola r = 4py, p> 0, with focus F(0, p). Let a be the angle…

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Q: The graph of 3 (x+y) = 25 (x -y²), shown in the figure, is a lemniscate of Bernoulli. Find the…

A: Given query is to find equation ifbthe tangent at given point.

Q: 4 Find a. the equations of the tangents to the circle x + y +4x - 2y - 24 = 0 at the points where…

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Q: Use this to find the equation of the tangent line to the parabola y = 3x² - 2x + 7 at the point (-2,…

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Q: d) A scalar equation of a line that goes through T(2, -5) and is perpendicular to the line 3x - 6y =…

A: The given line is: 3x-6y=5⇒6y=3x-5⇒y=3x-56⇒y=12x-56 which has a slope m=12.

Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

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Q: Find the exact length of the curve y2 = 16(x + 1)3,   0 ≤ x ≤ 3,  y > 0

A: See the attachment

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Consider the given equation as x=t3....(1) And y=t2....(2)

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z =x^2 +3y^2,…

A: z=x2+3y2 , x=1 at the point (1,2,13)

Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Determine the constant c such that the straight line joining the points (0,3) and (5.-2) is tangent…

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Parametrization is a way to change the parameters of a expression in such a way that domain of the…

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

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Q: 13. Find the equations of both lines that pass through the point (2, – 3) and are tangent to the…

A: We need to find equations of tangent lines.

Q: 15. Find the equations of the tangent lines to the parabola у%3D —х2 + 5х — 6 | At its points of…

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Q: An equation of the line tangent to the graph of f(x) = -x(1 – 2x)³ at the point (1,1) is a. y = -7x…

A: f(x) = -x (1-2x)3  f'(x) = -3x(1-2x)2 (-2) + (1-2x)3 (-1) f'(1) = 6(-1)2 +1 f'(1) = 7   Slope m = 7…

Q: Which of the following defines an equation of a plane curve that does NOT have a vertical asymptote?…

A: Given:  We have to find the equation of plane curve which has no vertical asymptote.

Q: Find the tangent lines as directed. To the parabola y=6x-3 perpendicular to the line x+3y=7

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Q: The (1) is given by the equation (1) : y = -2x + 3 and let (P)y = x2 + 3.x +1 be a parabola. 1. Find…

A: Answer :

Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: 45. Find the coordinates of all points on the graph of -1-2at which the tangent line passes through…

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Q: (a) If G(x) = x2 - 5x + 5, find G'(a) and use it to find equations of the tangent lines to the curve…

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Q: 1. Find the equation of a curve that passes through the origin and satisfies (1 + x²)y' + 2xy = 4x²

A: Given differential equation is  1+x2dydx+2xy=4x2 Simplify the given differential equation we get…

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1+x²)y' + 2xy 4x2

A: To find the equation of the curve

Q: II. Find the equations of the tangent and normal lines at the point indicated. a. 7x - 6V3ry + 13y -…

A: Solution is given below:

Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

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Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: If f(x) = 3x2 – 2x + 5, find f'(2). %3D Use this to find the equation of the tangent line to the…

A: Topic - slope and equation of tangent line

Q: 4) Given :y = ax + bx +1, the curve touches the line x+ y = 0 at %3D The point (3,-3). Find the…

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Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A…

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1)…

Q: 2. Consider the curve in the plane whose equation is 2x2 + 2xy + y = 2. (a) Find the x-intercepts of…

A: X intercept is the point where curve touches the x axis. So to find x intercept put y=0 in the…

Q: 1. Find the Cartesian equation of the curve represented by x = 4t + 3 and y 16t - 9, -0 <t<o.

A: Try to eliminate 't' to establish relation between x and y.

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: 1 Let P be the parabola with equation y Lx2, L be the line with equation y = V3 7. 3 1 and M be the…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: 1. Let P(x1, Y1) be a point on the parabola x?: be the angle between the parabola and the line…

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Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: Use implicit differentiation to find the points where the parabola defined by 2-2ry+ y -8z + 4y + 20…

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Q: A parabola has an equation of x² = 6y + 10. Compute the equation of a tangent to the curve which has…

A: Given that a parabola has an equation x2=6y+10. Here we have to compute the equation of a tangent to…

Q: 2. Find the equation of the tangent line to the parabola 2y^2+36x=0 which is parallel to the line…

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