A curve passing through (1, 0) is such that the ratio of the square of the intercept cut by any tangent off the y - axis to the subnormal is equal to the ratio of the product of the coordinates of the point of tangency to the product of square of the tangent and the subtangent at the same point.Determine all such possible curves.

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Prove that the point of the tangent intercepted between the axes at any point on the curve xmyn=am+n…

A: Prove that , The point of the tangent intercepted between the axes at any point on the curve…

Q: Find the slope of the tangent line to the graph at the given point. (4 – x)y? = x³, (2, 2) Cissoid:…

A: Slope of tangent line =dydx(4-x)y2=x3differentiating w.r.t 'x'y2d(4-x)dx+(4-x)dy2dx =…

Q: Find the slope of the tangent line to the graph at the given point.

A: Slope of the tangent line is the derivative of the given function at the given point. So…

Q: The slope of the tangent line to the graph of f(x) D x2 at a = -1 is: %3D %3D

A: Given  equation of the graph  f(x) = xx2-x                        ...........(1) We have to find the…

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Q: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

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Q: two curves are orthogonal at the point of intersection, if the tangent there cross at right angle…

A: It is given that the two curves are orthogonal at the point of intersection. So, the tangent is…

Q: The product of all the values of x for which the tangent lines to the graph of y= are parallel to…

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Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: Find the length of the curve y2 = x3 from the origin to the point where the tangent makes an angle…

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Q: Pls help ASAP

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Q: Find equations for the tangent lines to the graph at the given points. 7ху + x %3D 8, (1, 1) and (8,…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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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: The Slope of the tangent line to the at the point C7,3) is: Curve y=

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Q: Show that the tangent lines to the graph of y = (ex - e-x) / (ex + e-x) atx = 1 and x = -1 are…

A: Here we have to show that the tangent lines to the graph of y=ex-e-xex+e-x at  x=1 and x=-1 are…

Q: Find the points on the graph of x^2+2x+4y^2=4+y where the tangent line is horizontal

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Q: Find the slope of the tangent line to the curve — 4г* + 4гу + 4у — 92 at the point ( – 1, 3).

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Q: Prove that the point of the tangent intercepted between the axes at any point on the curve x…

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Q: Find the slope of the tangents to the curve at the points (P1 and P2) where it crosses the x-axis.…

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Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

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Q: Find the slope of the tangent line to the graph at the given point.

A: Slope:  The slope of a line measures the steepness of the line. The slope is calculated by rise over…

Q: Find the​ x-coordinates of all points on the curve y = (-x^2+4x−3)^3 with a horizontal tangent…

A: We know the slope of the tangent where it is horizontal is 0. we will need to find the derivative of…

Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: Find the tangent line to the Witch of Agnesi (graphed here) at the point (2, 1). 8 y + 4 (2, 1) 1 2…

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Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

Q: Find the slope of the tangent line to the graph at the given point. (4 - x)y? = x3, (2, 2) Cissoid:

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Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Find the tangent line to the Witch of Agnesi (graphed here) at the point (2, 1). 8 y = x + 4 (2, 1)…

A: y = 8 / (x2 + 4) point (x1, y1) = (2, 1)    equation of the tangent line: (y - y1)= m(x - x1)

Q: Determine the tangent to the curve 3y2 = x3 at (3,3) and calculate the area of the triangle bounded…

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Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

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Q: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

Q: Find a point on the graph of the curve y = (x - 3), where the tangent is parallel to the chord…

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Q: Find the x-coordinate of the point at which the tangent to the curve x > 0 is horizontal. Give the…

A: Here, we need to find the x-coordinate of the point at which the tangent to the curve y=xx5, x>0…

Q: Find the point (xo, yo) on the graph of y = x + 3x2 + 5x – 3, at which the slope of the tangent line…

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Q: x4 C: y=-+ 3 x3 17 4 12

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Q: The slope of the tangent line to the curve C at the point (1, 2) is (A) 4 (B -2 c) 2 D -4

A: Solving the problem by finding the slope of the tangent.

Q: Find the cuaatune of the curve dlefied by 1I cost Sin whore is

A: In the given question we have to find the curvature of the curve r→(t)=1rcost,1rsint,0where r>0…

Q: दलालभ यला Find an equafion of the tangent line to the ceurve at the grven point. y=x3-3x + 1, (2,3)

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Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the (x- 6) line y= 6x…

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Q: Let ℓ be the tangent line to the parabola y= x2 at the point (1 ,1). The angle of inclination of ℓ…

A: Given equation of parabola,y = x2       ................(1)Slope of line l is m,m = tanϕ = dydxat…

Q: At a maximum or minimum point, the tangent line to a curve is A. parallel to the x-axis C. parallel…

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Q: Find the tangent line to the graph of x (x² +y² ) = y² at the point

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Q: Find the family of curves in the plane such that in each point P(x,y) of it, the intercept of its…

A: Write the equation of the tangent for the family of curves for any point P (x , y). Assume the slope…

Q: Find the tangent line to x^6 + y^6=2 at (1, 1).

A: Given : x6+y6 = 2

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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