Find the equation of the set of points which are equidistant from (3,10) and the x-axis `y-x -5)²+3 O B. y-10=20(x-3)² OC. 1 y= 20 OD. 1 y=- (x- 3)²+5 20

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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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: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

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…

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

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Q: What are the equation of line passing through (-1,3) that is tangent to the curve x^2 + 4y^2 – 4x –…

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Q: To find the length of the curve defined by y = 5x° + 8x from the point (-1,-13) to the point (2,56),…

A: Here the curve is given by y=5x3+8x x coordinate of the points (-1,-13) and (2,56) are -1 and 2…

Q: Find equations for two lines that are both tangent to the curve y = x³ – 3x² + 3x – 3 and parallel…

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Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is parallel to the line y…

A: Given curve is y=2x3-3x2-12x+20 Given line is y=2-12x=-12x+2  Slope of the given line is -12.…

Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

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

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Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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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: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is perpendicular to the…

A: Given: The curve is y = 2x3 - 3x2 - 12x + 20 and the tangent line is perpendicular to the line y =…

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

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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: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

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Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: Determine the equațion of a line that is perpendicular to y=x+5 that goes through the point (5,-2)…

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Q: Find the equation of the tangents: y=x² + 6x² + 10x + 8 parallel x-y= 2. to the line А.…

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Q: find the point p on the line y=5x that is closest to the point (78,0). what is the least distance…

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Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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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: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: What are the coordinates of the points in the graph of y – z² + 6z – 13 = 0 in which the tangent…

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Q: The line y = 3x+7 and the curve xy-x = 4 intersects at the points A and B Show that the equation to…

A: Given Data: Equation of the line: y=3x+7 ......(1) Equation of the curve: xy-x2=4 ......(2) The line…

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: Find an equation for the set of all points (r, y, z) equidistant from point 10.) (1,0, 2) and the…

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Q: The curve y=ax²+bx+c passes through the point (2,28) and is tangent to the line y=4x at the origin.…

A: Given, y=ax2+bx+c

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: Find the point P on the line y=3x that is closest to the point (40,0). What is the least distance…

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Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

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

A: Note that the slope of a horizontal line is zero. Also the slope of a tangent is given by the…

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

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: Find the equations of the tangent lines to the circle x2 + y2 = 9 which pass through the point (-7,…

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Q: Find the equation of line passing through (5, 8) and perpendicular to y - axis. Oy = 5 Oy= 3 Ov=0 Oy…

A: The general equation of the straight line is: y=mx+c Now, the slope of the y-axis is infinity. So,…

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

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Q: Show that the locus of the point whose distance from Y-axis is thrice it's distance from (1,2,-1) is…

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Q: A line that is normal to the curve x^2+3xy-4y^2=0 at (6,6) intersects the curve at what other point?

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: Given the equation of the motion of the object 1 and object 2 are s1 = 2t2 - 3t , s2 = 3t - t2

Q: Find equations of both lines that are tangent to the curve y = x3 - 3x2 + 3x - 3 and are parallel to…

A: The given curve is represented by y = x3 - 3x2 + 3x - 3 and are parallel to the line 3x - y =…

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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Q: Find the orthogonal trajectories of the family of parabola described by the equation (x+2} = cy.…

A: Explanation of the answer is as follows

Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

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Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

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Q: Find equations of both lines that are tangent to the curve y=x3 -3x2+3x-3 and are parallel to the…

A: Given, curve y=x3 -3x2+3x-3 and tangent are parallel to the line 3x-y=15.