6. There equations. are two line through (-2,0) tangent to the parabola y = 4r. Find their

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: 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: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

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: For what values of a and b is the line 5x + y = b tangent to the parabola y = ax? when x = 4?

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

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: Find the equation of one of the tangent lines to the circle x^2 + y^2 = 5^2 that passes through the…

A: Here, to find the equation of the tangent line to the circle  x2+y2=52⇒x2+y2=25...(1) that passes…

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

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: 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: Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 6 that pass through the point…

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Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: For what values of a and b is the line 2x + y = b tangent to the parabola y ax? when x = 2?

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Q: Find the equations of the tangents to the curve x = 9t2 + 6, y = 6t3 + 3 that pass through the point…

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Q: What are the coordinates of the points in the graph of y-x+6x-13=0 in which the tangent line is…

A: Given query is to find the point where tangent line is horizontal.

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

A:

Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

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

A:

Q: Find the equations of the tangents to the curve x = 6t2 + 2, y = 4t3 + 2 that pass through the point…

A: Given data:     The first equation is: x=6t2+2. The second equation is: y=4t3+2. The given point is:…

Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

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

A:

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

A:

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

A:

Q: The slope of the tangent line to the parabola y 2x2 + 2x + 4 at the point (0, 4) = The equation of…

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Q: The slope of the tangent line to the parabola y = 3x + 3 + 4 at the point (5, 94) is: 33 The…

A: Equation of parabola y=3x2+3x+4 The slope of the parabola at any point is calculated as  dydx=6x+3…

Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

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Q: Find equations of both lines through the point (-2,-18) that are tangent to the parabola y = x² + 3x

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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: 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: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: . Find the equations of both lines that pass through the point (2, –3) and are tangent to the…

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Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y=-x^(2)+4x.…

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Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

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

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Q: What are the coordinates of the points in the graph of y-x+6x – 13=0 in which the tangent line is…

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Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 4?

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

A:

Q: What are the coordinates of the points in the graph of y-x²+6x – 13=0 in which the tangent line is…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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 equation of one of the tangent lines to the circle x2 + y2 = 52 that pass through the point…

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Q: Find the equations of the tangents to the circle x² + y² = 9 with slope 1

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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: 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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