The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

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: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

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Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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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: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

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Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

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Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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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: The slope of the tangent line to the parabola y = 2x + 5x + 7 at the point (- 4, 19) is: The…

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Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

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

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

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: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

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Q: find the tangent line to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

Q: 2. Find the equations of both the tangent lines to the parabola y through the point (3, 16). :-

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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: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: Find the parabola with equation  y = ax2 + bx  whose tangent line at  (1, −1)  has equation  y =…

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Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: Find the equations of the tangent lines to the parabola y = -x² + 5x – 6 at its points of…

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Q: 1 ,-8 5) /17 - V17 1- v17 1- V17 y = 2(x + 2 y = 2x 2 2

A: Given :           The vertex of parabola is V12, -812.  To find the equation of a parabola which…

Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

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Q: The slope of the tangent line to the parabola y 3x? + 6x + 2 at the point (- 2, 2) is: The equation…

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Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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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: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

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Q: 9) Find the slope of the tangent line to the hyperbola defined by the equation y2 - x2 = 7 at the…

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Q: Find the equation of the tangent to the 2(x² + y²)² = 25(x² – %3D - y²) at (3,1)

A: Given : 2x2+y22 = 25x2-y2

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: 6. Find the equation of the tangent line to the parabola y 2.x2 – x + 3 at x = 2. %3D -

A: Equation of given parabola is, y = 2x2 - x + 3

Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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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: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

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Q: Find equations of both the tangent lines to the ellipse x2 + 4y² = 36 that pass through the point…

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Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: Find the parabola with equation y = ax + bx whose tangent line at (1, 1) has equation y = 5x - 4.

A: ven parabola , y =ax2+bxtangent ,           y = 5x-4comparing with y = mx+c , slope of tangent m = 5

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: Find the equation of the line that is tangent to the curve y =-3e* at x = In 2. %3D

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Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: Find equations of both tangent lines to the graph of the ellipse x2/4 + y2/9 = 1 that pass through…

A: We have given equation of curve x24+y29=1 and point 4,0 We will find slope of tangent at any point…

Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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