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Q: An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the…

A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: There is a line through the origin that divides the region bounded by the parabola y = 7x X-axis…

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Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

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Q: When Spherius dips through Flatland, his cross section appears as a circle whose circumference is…

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Q: Line L is perpendicular to the line 6z – y = 7 and passes through the point (0, 6). Line M is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find an equation of the line through the point ( 3, 5 ) thatcuts off the least area from the first…

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Q: What is the point (0, 0) called?

A: To find,   The point (0,0) called

Q: The equation of the tangent line to the circle x^2 + y^2 = 36 at the point (5, square root 11) is…

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: the guidelines of this section to sketch the curve: y = x+ – 8x

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Q: Next There is a line through the origin that divides the region bounded by the parabola y = 4x –…

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Q: Point (x ,y) distance from Q А (5,5) (2,3) (1,1) V20 В 1 C 6. A 5

A: Given: A(5,5) B(2,3) C(1,1) AQ=20 BQ=1 CQ=2

Q: Find the equations of the tangents to the curve x = 6t2 + 2, y = 4t3 + 2 that pass through the point…

A: Given data:     The first equation is: x=6t2+2. The second equation is: y=4t3+2. The given point is:…

Q: Find an equation of the line through the point (3,5) thatcuts off the least area from the first…

A: The line with slope m (where m < 0 through (3, 5)).

Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

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Q: ie point where x (-)- %3D

A: Maxima and minima: f(x)=x2+kxWe should find the value of f'(x) Then we calculate the value of x for…

Q: Find equations of both lines through the point (5, –6) that are tangent to the parabola y = x2 – 3x

A: topic - equation of tangent to curve

Q: If the point (6, -1) is reflected over line y = 2 then dilated by 2, what would the new points be?

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Q: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

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Q: The slope of the tangent line to the parabola y 3x2 + 2x + 6 at the point (5, 91) is: The equation…

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Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: Ly Use the definition of

A: Use the definition of differentiability to prove that if f is differentiable at a,b, then f is…

Q: d) At what angle above the horizontal does the trajectory begin in that direction?

A: Given: Suppose you go up a hill whose shape is given by the equationz = 1000 - 0.005x2 - 0.01y2,…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: Find the slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: Find the point on the curve y=lnx such that the tangent line pases through the point (2,4). Need to…

A: Given The equation of curve is   y =ln x The tangent line passing through (2,4)

Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: Determine the equation of the line passing through the point (3,22) which minimizes the area of the…

A: This question is based on application of Derivative. The two-point form of a line passing through…

Q: Define “hyperbolic” trajectories?

A: we have to define "hyperbolic" trajectories

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: Write the equation of the circle of radius 5 that istangent to both axes and passes through the…

A: Write the equation of the circle of radius 5 that istangent to both axes and passes through the…

Q: or 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: A seismological station is located at ( 0, -2) , 2 km away from a straight shoreline where the…

A: From the given data, If the earthquake was determined 5 km from the station, that means it could be…

Q: Give the equation of a circle tangent to the line 3x + y -2 = 0 at (-1, 5) and with a radius equal…

A: Topic = Circle

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: The slope of the tangent line to the parabola y 3x + 3x +7 at the point (- 5, 67) is: The equation…

A: Take the derivative and put the given point.

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−6x2 and the…

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Q: What point on the curve y = x is closest to the point (5, 0)?

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Q: 1. The point (5,2) lies on the curve y =Vx-1. Find the slope (correct to six places) of the secant…

A: Since you have posted a question with multiple sub-parts, we will solve first three Sub-parts for…

Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: What is the slope of the tangent line to the graph of the solution of y' = 3√√y + 7x³ that passes…

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 1 which pass through the point (-4,…

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Q: The equation of the tangent line to the curve X2+y2=169 at the point (5,-12) is

A: