A line meets a curve y=2x-1 at the point (5,4). The line is tangent to the circde C:x +y² +10x+8y+ p=0. The equation of the nomal to the circle at the point where the given line is tangent, is:

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

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A: This problem is based on a variable separable first order ordinary differential equation. We have to…

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

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Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: Find the length of arc of the curve 9y^2=4x^3 from the origin to the point (3,2 squareroot of 3)

A: The arc length of a curve y=f(x) from x=a to x=b is defined by the integral L=∫ab1+dydx2dx.

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

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Q: The curve y=ax^2+bx+c passes through the point (1,9) and is tangent to the line y=3x at the origin.…

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Q: Q4\ Find an equation for the tangent line drawn to the circle (x- 3)2 + (y + 3)2 = 50 at the point P…

A: We Know that A tangent to a circle at point P with coordinates is a straight line that touches the…

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Q: Given the curve y² = 5x – 1 at point ( 1,-2 ) , find the equation of tangent and normal to the…

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Q: Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the…

A: We begin by finding the points(s) of intersection of the 2 curves y =x2+7x+6  &amp;  x-2y = 6y…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: 1) Given the curve 2x? + y3 = x3 + y? find the x-intercept of the tangent line at the point (2,1)

A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

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Q: Find an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

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Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

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Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: Find the slope and concavity of the curves at the given points. r = eθ, θ = 0, π

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

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

A: Given, The curve  y=ax3+bx2+12x-7 We have to find the value of a  and b such that tangent to the…

Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: The curve y = ax + bx +c passes through the point (1,9) and is tangent to the line y = 4x at the…

A: Please see the answer below.

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

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Q: Find the equation of the curve, in the XY plane, that passes through the point (2, 2) and is such…

A: Differential equation

Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x² + y²)² = 25(x² – y?) at the…

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Q: 3x + xy? 2y + x?y dy dx

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Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

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Q: B. Find the slope of the curve at the point indicated. 1. y = at x = -1 4-x2 %3D 2x+3 2. y = xv1 +…

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Q: a. Determine the points where the curve 5x + 3y - y= 5 has a vertical tangent line. b. Does the…

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Q: Find equations for the tangents to the circle (x - 2)2 + ( y - 1)2 = 5 at the points where the…

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Q: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: 4.For the 2 curves xy = 8 and x2 = 64y, find the angle between the two tangent lines at the !! %3D…

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Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

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Q: 2. Consider the curve in the plane whose equation is 2x2 + 2xy + y = 2. (a) Find the x-intercepts of…

A: X intercept is the point where curve touches the x axis. So to find x intercept put y=0 in the…

Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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

A: Explanation of the answer is as follows

Q: 27. The equation of the common tangent to the circles x+ y - 12x- 2y-123D0 and x*+y - 4x + 4y + 4 0…

A: Note: "Since you have asked multiple questions, we will solve the first question asked by you. If…

Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: a. Determine the points where the curve 4x + 2y -y =1 has a vertical tangent line. b. Does the curve…

A: Consider the given curve 4x + 2y2 – y = 1

Q: A parabola has an equation of x² = 6y + 10. Compute the equation of a tangent to the curve which has…

A: Given that a parabola has an equation x2=6y+10. Here we have to compute the equation of a tangent to…