For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

Q: Find the tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

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: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

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 length of the curve y x² Inx 8 at (2 <x< 4)? -

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Q: Find the equation of the family of curves whose at any point (X, Y) is 1. 3x? + 4 2. * y X+1 3. y-1…

A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: A coordinate of the point on the curve of y=2x3−3x−6, where the tangent at the point is…

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Q: Find the point Q that is on the curve nearest %3D the point (4, 1)

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Q: For what values of a and b is the line 2x + y = b tangent to the parabola y ax? when x = 2?

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Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

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 formulas for the distances between (0, 0) and (a, a2 ), a &gt; 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: y = 4 1 ,2 In x, 1<x < 2 2 -

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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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: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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Q: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

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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: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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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: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

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Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

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

Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

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

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

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: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

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Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: 3. Find the length of the curve y = x - In a, 1< x < 4.

A: Note: According to bartleby we have to answer only first question please upload the question…

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: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

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