2: Show that the line equation passing through two distinct points (a1, b1) and (a2, b2) can be given as T y 1 a1 bi 1= 0. a2 b2 1

Q: 6. If x(t) = e' +1 and y=2e²ª are the equations of the path of a particle moving in the xy-plane,…

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Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: What is the equation of the line that is paralel to y-3r+ 12. passing through (4, 2), witten in…

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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: Find the solutions to y = −2y + 8 satisfying y(0) = 3 and y(0) =4, and sketch their graphs.

A: The given differential equation is y' = -2y + 8, satisfying the initial condition y(0) = 3, y(0) =…

Q: Find the equation of the line tangent to Y 3x2 + x + 1 at x = -3. у 3 —17г — 26 O y = 6x – 3 O y =…

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Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

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: Find the equations for all the lines tangent to x + y° – y= 1 at x = 1. r+ y³ – y = 1 2

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Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

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Q: Suppose that these two lines are the paths of two particles. If t and s measure ime in seconds, and…

A: We have given the equations of two lines : l1 : x,y,z=2+2t,8+t,10+3t l2 : x,y,z=5+s,12-2s,17-s…

Q: The line which is parallel to r + 3y – 5 = 0 and normal to the curve f(x) = a - 1 at a point in the…

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Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

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Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: 3. Which equation passes through the point (1, -2) and is perpendicular to y = x O y = 3x - 1 O y =…

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Q: Show that a linear equation dy a(x) + b(x)y = c(x) %3D dx is exactif a' (x) = b(x).

A: A differential equation of type  P(x,y)dx + Q(x,y)dy =0 will be an exact differential equation if…

Q: 1. XY is the same as YX. 2. XY is the same as YX. 3. HAB and AC are opposite rays, then they are…

A: As per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

Q: Write the equation of the line tangent to the curve x In y+7xy = 28 at the point (4, 1). 32 y-7x 60…

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Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

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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…

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Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: The cartesian equation of the curve x = VE ,y = 1-t is: (a)y = 1-x2, x20 (b)y = 1-x ,x20 %3D (c) x =…

A: Cartesian equation is a equation which involves x and y , just I have eliminate the t from given…

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

A: The given curve is in paramatric form as following- x=√t y=1-t Where t is a parameter. To find the…

Q: 1. Select all the equations on which the point (10,0) lies. A. 5x +2y: 15 B. 2x +4y = 20 %3D C.x +6y…

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Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: y = mx + b is called the v ---Select--- rm of the equation of a line. standard Additional Materials

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Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

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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: The cartesian equation of the curve x = 1-t.y vt is: (a)y = 1-x, x2 0 (b)y = 1-x .x 20 (c) x=1-…

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Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

Q: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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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: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 4? a = b…

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Q: An insect is in a toxic environment. The level of toxicity is given by I(x,y)= 2x* – 4y If the…

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Q: 5. Identify the following curve equations: a. 4y -3x2 + 5x - 7= 0 b. 9x2 - 4y2 36 3x2 +4y2 0 d. 4x2…

A: a) since 4y-3x2+5x-7=0 has the heighest degree of x is 2 but the heighest degree of y is 1.So it is…

Q: The equation of the tangent to the curve y = x4 – 4x3 + 2x? – 4x + 15 that is perpendicular to the…

A: topic - equation of tangent line to curve

Q: Given the curve y= x^3 - 4x + 1 . Find the equation of the line perpendicular to that curve at…

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Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

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

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Q: X. xy ds where C is the straight line from (2,3) to (4,0).

A: Given: The curve C is the straight line from 2,3 to 4,0, To find: The value of ∫Cxy2ds.

Q: For what values of aa and bb is the line −4x+y=b-4x+y=b tangent to the curve y=ax2y=ax2 when…

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Q: . Solve the following problem (a) Y'(t) = XY(t) + 1, (b) Y'(t) = \Y(t)+t, Y(0) = 1. Y(0) = 3.

A: In this question, we will solve the given linear first order differential equations.

Q: Eliminating the parameter from x = f(t) and y = g(t) means eliminating_______ from the pair of…

A: In parametric equations are the quantities are represented by the functions of a single independent…

Q: S. 3 z dz where C is straight line segment from i to -2 - 3i

A: We put z=x+iy And dz=dx+idy

Q: Determine the equation of the curve which is perpendicular to the line joining any point on the…

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