Find the points on the curve 9y = x where normal to the curve makes equal intercepts with the axes.

Q: Find the equation of tangent and normal to the curve y= 3x2 - 4x+5 at (– 1, 12)

A: Given the equation y=3x2−4x+5

Q: Find the points on the curve where the tangent is horizontal or vertical. x = - 3t, y = t² - 8…

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Q: Find the slope of the tangent line to the curve - 3a? + xy + 3y³ = 45 at the point (– 3, 3).

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Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: Find equations of the tangent and normal line to the curve x? – xy – 3y2 = -4 at (1,2).

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

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Q: Find the ponits on the curve 9y2 =x3 where normal to the curve makes equal intercepts with axes

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Q: Find the equations of the tangent and normal lines to the curve y=x²-2x-3 that is parallel to the…

A: The given equation of the curve {parabola} is y=x²-2x-3  and the given equation of the straight line…

Q: Find the tangent and normal to the curve y=2e-x/3 at the point where the curve meets the y-axis

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Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: y = x3 + 6x² + 9x – 2 at x = 0 -

A: topic - equation of tangent and normal Line to the curve

Q: Find the equation of the line tangent to the curve 3t2 + 8,y = 8t + 3 at t = 2

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Q: find equation for the lines that are tangent andnormal to the curve at the given point.xy + 2x - 5y…

A: Given : The equation is x y + 2x - 5y = 2 and point (3, 2).

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: Find an equation of the form y = f(x) for a curve with r-intercept 2 whose tangent line at any point…

A: Here, to find the equation of the curve of the form y=f(x) with x-intercept 2. That is curve passes…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given Data The equation is:  The point is: (-2,1)   Substitute the point (-2, 1) in the given…

Q: Find the ponits on the curve 9y2=x3 where normal to the curve makes equal intercepts with axes

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Q: Find the equation of the tangent and normal line at the point indicated. Sketch the curve. y = x –…

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Q: The equation of the tangent line to the curve +y =64, at (6,-12) is 12 y=D (-6)+12 6. 6. 12 -6) – 12…

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Q: Find the point(s) on the graph of y = (x2 – 168)e where the tangent line is horizontal.

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Q: Find the equation of the line tangent to the curve x = 3t2 + 8 , y = 8t + 3 at t = 2

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Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у)…

A: Solution ) given f(x) = y = 2x3 + 3x2 - 12x + 1 f'(x) = 2 × 3 × x3 - 1 + 3 × 2 × x2 - 1 - 12 + 0…

Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

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Q: Find an equation of the tangent line to the curve y=x√xthat is parallel to the line y= 1 +3x

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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.…

A: First find points P1 and P2 and than find the derivative at that points.

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: Find the equations of the tangent and the normal at the point indicated. y = x2 - 2x at its…

A: Given that - y = x2 - 2x at its points of intersections with the line y = 3

Q: Find the equation of the tangent and normal lines to the curve y=sqrt(x) at the point (1,1).

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Q: Find the slope of the tangent line to the curve 3z? – 2xy – 3y3 = 63 at the point (3, – 2).

A: topic - slope of tangent line to curve

Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: Find the equation of the line normal to x^3 + y^3 = 6xy at (3,3)

A: Given, x3+y3=6xy

Q: Write the equation of the line tangent to the curve xe = 6y + 7 at (7, 0). %3D

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Q: Find the point on the curve y=/2 for which the tangent ine to the curve is perpendicular to the line…

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Q: At what point on the curve x = 9t2 + 6, y = t3 − 9 does the tangent line have slope 1/2?

A: Given parameteric equations of curve,   .x = 9t2 + 6 , y = t3 – 9   To find the point on curve…

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 the equation of the tangent and normal line using the stipulated conditions   2.) x2 + 2y2 =…

A: The equation of tangent line is x2+2y2=9⇒x29+y292=1we have a=3 and b=92Since, we know that the…

Q: Find the equation of the line that is normal to the curve (y-x)2 = 2x + 4 at (6,2). %3D

A: Use equation of normal line

Q: What is the slope of the line tangent to the curve y = 3x² + 6x +3 at x = 4? Oy' = 51 O y' = 30 O y'…

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Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. y = x3 –…

A: We have to solve the problem

Q: Find the equation of the line normal to the curve 2x^2-3xy+y-18=0 at (3,0).

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Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

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Q: At what point on the curve x = 3t2 + 1, y = t3 – 5 does the tangent line have slope ? 2

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Q: For what value(s) of x is the line tangent to the curve y = xV6 - x horizontal? Vertical?

A: Given curve is: y=x6-x Differentiating with respect to x we get,…