a) Given that straight line y + x=2 is tangent to the curve y =x² – 6x + q. Find value q.

Q: a particle moves along a curve y = (2x² + 5x)°, calculatey (0) and what is the interpretation of the…

A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

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: For what value of x does the tangent line to the curve y=7+3e^x−6x  is parallel to the line 8x−8y=9?

A:

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

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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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: Find the exact length of the curve. 글 cosh(2x), sxs8 y = 4 +

A: Given:

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: 3. Find the points where tangent lines are vertical or horizontal: x³ + y³ = 6xy

A: Given:- x3+y3 = 6xy To find :- Points where tangent horizontal and vertical

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: Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 6 that pass through the point…

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Q: Find the point on the curve y=x√x for which the tangent line to the curve is perpendicular to the…

A:

Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

A: We are given a curve and we need to find out the slope to the tangent line at the point (1,-4). For…

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

A:

Q: At what point is the tangent line to the curve y3=2x2 perpendicular to the line x+2y-2=0? P= (?,?)

A: We have to find the point

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

A:

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 sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: find the tangents as direccted to the curve y = x4 – 4x3 + 2x2 – 4x + 15, perpendicular to the line…

A: Given that  y=x^4-4x^3+2x^2+4x+15  Line is x+8y=7

Q: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

A:

Q: At what point on the curve y = 2x²– 3x – 1 is its tangent parallel to the line y = 5x + 2?

A: Given curve is : y=2x2-3x-1 And the given line is : y=5x+2 We need to find the point on the curve at…

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

A: Given Data The equation is:  The point is: (-2,1)   Substitute the point (-2, 1) in the given…

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

A:

Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: 4. Find the equation to the tangent line to the curve -3 %3D at the point (x, y) = (1,2).

A:

Q: a, given that the line ax+y+1 = 0 is tangent to the grapl

A: We have to find the value of a according to the given information

Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

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Q: What is the equation of the line tangent to the curve 9x^2 + 25y^2 – 225 = 0 at (0, 3)?  a. x + 3 =…

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Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

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

A:

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: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

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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: x4 C: y=-+ 3 x3 17 4 12

A:

Q: At what point is the tangent line to the curve y = 6x² perpendicular to the line x + 2y – 8 = 0?…

A: Follow next step

Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

A:

Q: At what point is the tangent line to the curve y = 2x to the line x - perpendicular – y – 8 = 0?…

A: Let the point is (a, b), so the slope of the tangent line to the given curve can be determined as,…

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

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Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

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Q: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

A:

Q: Find the tangent lines to curve x² + 2y2 = 9 that is perpendicular to line 4x – y = 6? %3D

A: Given the equation of line is 4x-y=6.   Rewrite the equation in slope intercept form. y=4x-6   Thus,…

Q: What is the slope of the line tangent to the curve y = 3x² + 6x +3 at x = 4? Oy' = 51 O y' = 30 O y'…

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Q: Find the exact length of the curve. 36y² = (x²-4)³, 5≤x≤9, y 20

A:

Q: For what value(s) of x is the line tangent to the curve y = xV6 - x horizontal? Vertical?

A: Given curve is: y=x6-x Differentiating with respect to x we get,…