(d). Consider the line y = ax , where a is a positive constant. What is the shortest distance between the line and the point (a, 0) ? (a) (b)- 1 (c). (d). Ta Va?+1

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

A:

Q: the sloper of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

A: 1) Find dydx at the given points to find the value of 'a' . 2) Now satisfy the point (1,-1) to the…

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Q: Find the shortest distance from the point x = (-3, 0, -12)  to the line r = t(0, -2, -2).

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Q: the slope of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

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Q: Find the distance from the point to the line. (-4, – 2,1); x= 5 – t, y = 1- 2t, z = - 6 + 3t

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Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

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Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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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: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

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Q: the slope of the curve 2y2=ax2+b at (1,-1) is -1.find a,b

A: The equation of the curve is  2y2 = ax2+b…

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A:

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: The slope of the line tangent to the graph of 3x +5In y 12 at (2, 1) is 12 (A) 12 (B) 5. (C) 12 4.

A: Given that 3x2+5lny=12To find : Slope of the tangent line at point 2,1Solution :

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the equation of a line tangential to the curve y = 2x² + 7x + 9 at P(1,18).

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Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

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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: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

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Q: Determine the slope of the curve x2+ y2– 6x – 4y – 21 = 0 at (0, 7).

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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: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

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

A: To find the points at which tangent line is horizontal , y' =0.

Q: 1. Find the DE of all straight lines with slope and y-intercept equal.

A:

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: What is the equation of the line tangent to the graph of y = (2x+3)/(3x-2) at the point (1,5)? 13x -…

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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…

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Q: What is the slope of the secant line that intersects the graph of h(x) = 16 – z at z = l and a = 4?

A: The slope of the secant line or any other line can be defined as the rise to the run ratio which is…

Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

A:

Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

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

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

A:

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 equation of a line normal to the curve x^2=16y at (4,2).

A: Solve the given problem.

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: Find the point on the line x + 2y = 5 that is closest to the origin.

A: Let the point (x, y) on the given line x+2y=5  is closest to the origin (0, 0). observe that…

Q: Suppose the curve y =x4 +ax3+ bx2+ cx +d has atangent line when x=0  with equation y= 2x +1 and…

A: Given the curve is   y =x4 +ax3+ bx2+ cx +d Differentiating with respect to "x" y' = 4x3 + 3ax2 +…

Q: Consider the line y = ax , where a is a positive constant. What is the shorteşt. distance between…

A: We need to find shortest distance,

Q: Determine the slope of the curve x2 + y2 – 6x – 4y – 21 = 0 at ( 0, 7 ).

A:

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: 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'…

A:

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: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…

Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

A: Here we use the general formula for calculating the shortest distance between line and point.