A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the c point-slope form for the line tangent to the circle whose equation is x +y =225 at the point (12,9).

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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Q: A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that…

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

Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

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Q: Find the points at which the graph of this equations has vertical or horizontal tangent lines:…

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Q: ) Find the slope m of the tangent to the curve y = 9 + 5x² – 2x3 at the point where x = a. 10а + 6а?…

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Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. 8x y at…

A: Solution

Q: Determine an equation of the line tangent to the curve at the given point. 4x² + 4xy + 3y 51, (3,1)

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Q: Find the coordinates of the point on the graph of y = x^2− x + 3 at which the tangent is parallel to…

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Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

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Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: A coordinate of the point on the curve of y=2x3−3x−6, where the tangent at the point is…

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Q: 2. Find the slope of parabola y = ²+3 at any point on the curve.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Find the coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: Find the equation of the tangent to the curve  y = -5x2 + 6x +7 at the point (1/2 , 35/4)

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Q: The slope of the curve defined by the equation y-x + x =-2 at the point (-1,0) is %D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the point on the graph of y = x3 such that the tangent at the point is parallel to the line y –…

A: Consider a graph: y=x3……1   Equation of line parallel to the tangent of above equation is:…

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line.…

A: Given equation of a graph is 4x2+y2-8x+4y+4=0 Since we need to find the points where the tangent to…

Q: Consider the curve x+y² +2xy=4x . (a) Find all the x-intercepts of the curve. (b) For each of the…

A: The given curve is: x3+y2+2xy=4x...(1)

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: Find the equation of the tangents to the graph y = x^3 + 3x^2 - 15x -20 at Ox-y-9=0 O9x-y-48 = 0 O9y…

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Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

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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 a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

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Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

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Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: Find the equation of the tangent line to the circle at the point (-3, -4). Equation of the circle *…

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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: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

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Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

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 an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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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: Find the equation of the curve whose slope at any point is In and which xy2 passes through the point…

A: Point (x1 , y1) = (1, -2) Slope = ln1xyxy2

Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: Consider the curve given by y = 3x* – 6x2 + 2, a. Find the slope of the curve at the point whose x…

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Q: Does the parabola y = 2x2 - 7x - 1 have a tangent whose slope is -1? If so, find the point of…

A: Recall: Slope , m= dydx Point - slope intercept form : (y-y1)=m(x-x1) ; where 'm' is the slope

Q: find the slope of the curve at the point indicated y = x - 1/x + 1, x = 0

A: Given, y=x-1x+1 and the point x = 0

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: 2. Find the slope of the curve y = 3x +1 at the point (-0). Draw the graph of the curve.

A: GIVEN y2=3x+1 at(-1/3,0) we need to find the slope of the curve and graph the curve

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: 2а3x at (a, a) ,2 x2+a²

A: Given curve is,

Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

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Q: a. Find an equation for the line perpendicular to the tangent to the curve y = x' - 9x + 4 at the…

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