1. Find the slope of the curve x+ y² -6x-4y-21 0 at (0, 7). Compute also the tangent line and normal line at (0,7)

Q: Find the condition that the line ax+by=1 may be a normal to the curve an-1y=xn

A: To find the condition of line ax + by = 1 which is normal to the curve a^(n-1) y = x^n

Q: 7. Find the slope of the tangent line to the graph at (1,1): x²y² – 9x² – 4y² = 0 %3D r-9r-4y = 0…

A: find the slope of the tangent line to the graph at 1,1; x2y2-9x2-4y2=0 differentiate the equation…

Q: Find the equation of the line tangent to the curve xy^3+xy=6 at the point (3,1). When the equation…

A: Firstly, we will find derivative And then we can solve for y'and we get

Q: Find an equation of the tangent line to the curve 2(z² + y°)² = 25(æ² – y³) (a lemniscate) at the…

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Q: Find the slope of the tangent line to the curve−4x^2+4xy−3y^3=−5at the point (1,−1).

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Q: Find the equation of the tangent line to the curvey = √2-4 at the point (5, 1). Oy=2-1 Oy= 22-2 Ov=z…

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Q: Find the tangent and normal line to the curve at the specified condition.  y = x ( 4x - 1 )2 at…

A: The tangent line is a straight line to the curve that touches the curve at a single point. The…

Q: Find the equation of the tangent line to the curve x + y² = 4 where the slope of the curve is 1.…

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: Find the equation of the tangent line to the curve 3y + 2x² = x²y² + 7 at (2, 1) .

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Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

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Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: Find the equation of the tangent line to the graph xy^2 − 2y = x^2 at the point (2, −1).

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Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find the equation of the tangent line and normal line to the graph of y = x-1 at the x+1 point where…

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Q: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

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Q: Verify that (4,1) on the curve x + /xy = 6 and find the lines that are tangent and normal to the…

A: Given that, the curve is x+xy=6. Differentiate the curve x+xy=6 with respect to x as follows,…

Q: Show that the curve of y = 2e2z + 3r + 2r3 has no tangent line with slope 2.

A: The given curve is y=2e2x+3x+2x3. Obtain first derivative as follows. dydx=ddx2e2x+3x+2x3=4e2x+3+6x2

Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

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 and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: Find an equation for the tangent line to the curve y = 4 at the point (3,16). X - 1 Oy - 16 = -3(x -…

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Q: Find the equation of the line tangent to the curve of x²y2 – xy + x = 1 at (1, 1).

A: Given: x2y2-xy+x=1 As we know that; The slope of the tangent line to the curve at a given point is…

Q: Find the slope of the tangent line to the curve 3x? + xy – 4y³ = 6 at the point (1, – 1).

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Q: Find the equation of the tangent line and the normal line of the following curves at the given point…

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Q: Find the equation of the tangent line drawn to the curve y - 4x* – 6xy = 0 at the point (-1,3).…

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Q: Find the slope of the tangent line to the curve x²-3y=4y³ at x=-1

A: Solution: Consider the given equation of the curve is: x2 -3y = 4y3or4y3 = x2  -3y Differentiating…

Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

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Q: Find an equation of the tangent line for the curve.15 y + (xy + 2) = 0 at the point (3,-1) 3x-7y 16…

A: equation of tangent line at point 3,-1 for graph or curve xy+23+y2=0

Q: FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. 1.…

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Q: Find the equation of the tangent line to the curve at the given point. y = v2x + I, (4, 3)

A: →Slope, m = dydx→dax+bdx =12ax+b→Equation of straight line passing through (xo,yo) with slope m is…

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: The curve y = [In (x + 4)]² has horizontal tangent line at the point(s)

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Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

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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 the points on the curve x^2y^2+xy=2 where the slope of the tangent line is equal to -1

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Q: 20. Locate the points on the curve xy (1 - x- y)2 where the tangents lines parallel to the x- axis.

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Q: Find the slope of the tangent to the curve x° + 4xy+ y² = 13 at (1, 2). The slope is (Enter undef if…

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Q: Find the equations of the tangent and normal lines to the graph of  (x^2 + y^2)^3 = 8x^2y^2 at…

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Q: I Find the equations of tangent and normal lines of the curves at given points: a. x3 + y2 – 3xy = 0…

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Q: 2. Find the equation of the tangent and normal lines at a given point on the curve. x²y² – 10y + 8x…

A: the equation of the given curve is: x2y2-10y+8x=0 the given point is (2,4) we have to find the…

Q: FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. 2.…

A: Given: x2y3-2xy=6x+y+1 To Find: Equation of the tangent line and normal line of the given curve at…

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: Find the slope of the tangent line to the curve 1x^2+1xy+4y^3=8 at the point (−3,−1)

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Q: 2. Find the slope of the tangent line to the curves: (a) xy + y³ = 12 at the point (2, 2), (b) 3x4/3…

A: This question can be solved using the concept of tangent and normal using application of…