0. Point P(6, 7) lies on the circle (x + 2)² + (y – 1)² = 100. What is the slope of the line that is tangent to the circle at P?

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: 2 Find an equation of the line L, where L is perpendicular to y =x and passes through the point…

A: Given a Line L which is perpendicular to  y = (2/3)x  at point (3,2)  Equation of line L is…

Q: Find the slope of the tangent line to the circle 4x² + 9y² = 36 at the point (0,2).

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Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

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Q: a curve like y=x/1+1x^2 is called a serpentine. Find an equation of the tangent line to the curve…

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Q: Find the point(s) on the graph y = x3 where the line through the point (4, 0) is tangent to y.

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Q: 8. What is the slope of the line tangent to the curve defined below at the point (1,1)? 1 -1 -2

A: The solution are next step

Q: The curve y = ax² + bx + c passes through the point (1,8) and is tangent to the line y= 6x at the…

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Q: 2. The slope of the tangent line to a curve at any point (x, y) on the curve is. What is the…

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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: 2) Find and sketch the circle of cur vature at the point on the curve y = x2 where the tangent line…

A: To find and sketch the circle of curvature at a point on the curve y=x2 , where the tangent line has…

Q: Verify that (2,3) is on the curve x²+xy-y²=1 and a. find the line that is tangent to the curve at…

A: Given curve, x^2+xy-y^2=1

Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4)

A: Equation of the tangent line

Q: 1. Find the equation of tangents to the circle x² + y² = 9 with slope 1.

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Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: At which points on the curve y = 1 + 40 x3  - 3 x 5  does thetangent line have the largest slope?

A: The given equation of the curve is y=1+40x3-3x5. The slope of this given curve is given by its…

Q: What is the slope of the line tangent to the curve defined by y +xy-x 11 at the point (2, 3)

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Q: 17. Given the curve y = 3x³ – 4x² +7, find the slope of the tangent line at the point when x= 3.

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: -1 Where on the curve y = (196 + x²)¯ does the tangent line have the greatest slope? NOTE: Enter the…

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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: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

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Q: Find the equations of the tangent lines to the circle (x + 2)² + (y + 2)² = 25 at the two points…

A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Q: The slope of the tangent line at any point (x, y) on a curve is 25 If the point (9, 3) is on the…

A: Explained below

Q: Try to find the slope of the tangent to the circle x²+y²=5. at the point (-2, 1) Show solution

A: tangent

Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

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Q: 5 Find the equation of line tangent the circle x+y = 25 at point (3, -4). .2 %3D

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Q: Between two telephone poles that are 30 feet apart, there is a wire suspended in the shape of a…

A: According to question, y = 40 cosh x40 -15,-15 ≤ x ≤ 15

Q: A tangent line to y=1/x^2 intersects the x-axis at the point A and the y-axis at point B. What is…

A: Please note: The line tangent to the given function intersects the x-axis at a point A and the…

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 the values of a and b if the tangent to y = ar² + bx at (1,5) has a slope of 8.

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Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: The slope of the tangent line at any point (x, y) on a curve is 25 If the point (9, 3) is on the…

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Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

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

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 15.)) What is the slope of the line tangent to the curve y +2 = - 2sin y at the point (2, 0)? 2 (A)…

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

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Q: Find an equation of the tangent to the circle x 2 + y 2= 25 at the point  (3,4)

A: x2+y2=25 Differentiating with respect to x, we get 2x+2y·dydx=0⇒2y·dydx=-2x⇒dydx=-xy Now slope of…

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

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Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: 4. Find the equation of the circle that is tangent to the line x = 8 that has a center at (-5, 10).

A: The general equation of circle having the center at h,k and radius r is given as, x-h2+y-k2=r2 it is…

Q: 6. Given the curve y = x/x at what point on the curve is the tangent parallel to the line 4x – y + 6…

A: We will use differentiation and slope of line to solve this.