At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a second time?

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: Find an equation of the normal line to the parabola y= x2 -5x +4that is parallel to the line  x-3y…

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: Show that the equation of the tangent line to the hyperbola                        x2/a2 − y2/b2 = 1…

A: Given Data The equation of the hyperbola is x²/ a²- y²/ b²=1. The points are (x0,y0).…

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

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Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

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Q: Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

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Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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Q: Find the points on the curve x^2y = 2 nearest the origin.

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Q: The slope of the tangent line to the parabola y= 4x2 + 2x + 4 at the point (-1, 6) is : ?  the…

A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

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Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

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Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: Find an equation of the normal line to the parabola y = x2 - 5x + 4 that is parallel to the line x -…

A: y=x2-5x+4 Differentiating with respect to x, we get dydx=2x-5 Now slope of the normal line is,…

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: The x-coordinate of the point where the tangent line to the parabola y=2x^2 at x=1 intersects the…

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Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)?

A: the equation of the normal line to the ellipse can be found by differentiating the given equation…

Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

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Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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Q: Find the equation of the line tangent to the ellipse x^2 - xy + 2y^2 - 4x + 2y + 2 = 0 if the…

A: given equation of ellipse x2-xy+2y2-4x+2y+2=0 and a line  4y-x+2=0 to find equation of line tangent…

Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

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Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

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Q: At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time?…

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)? O y =…

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Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

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Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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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: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.