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

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: Find an equation of the straight line having slope 1/6 that is tangent to the curve y=√x+5.

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Q: Find the equations of both lines that are tangent to the curve y = x - 3x2 + 3x - 3 and are parallel…

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Q: Find the equation of the curve for which y"= 2x³. The slope of the inflectional tangent at (-1, 3)…

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

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Q: =2(3x2)^ has two horizontal tangent lines. Find equations for both of them.

A: y=23x2xy'=2ln3x2+23x2xLet the tangent line equation is given byy-y1=mx-x1y-y2=m1x-x2m=m1=0...as…

Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

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Q: 6. Determine an equation of oNE of the two lines tangent to the curve x?y +2xy² = x + 6y, when x =…

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Q: The equation of the tangent line to the circle x^2 + y^2 = 36 at the point (5, square root 11) is…

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

A: Equation of tangents: y-y1 = m(x-x1) m=dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now do…

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: Find equations of the tangent lines (in slope-intercept form) to the curve y = x-1 that are parallel…

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Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

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

A: we have to find the equation of the tangent line

Q: Find the equation of the line tangent to the curve (x-2)^2=-4(y+3) at (2,-3)

A: Given data:     The expression for the equation of the curve is: (x-2)2=-4(y+3). The given point is:…

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: 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 equations for the lines that are tangent and normal to the curve at the point (1,1).. x³ + y² =…

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Q: Find equations of both lines through the point (5, –6) that are tangent to the parabola y = x2 – 3x

A: topic - equation of tangent to curve

Q: Determine an equation of the line tangent to the curve Y = 5x-4 at the point with x- coordinate 4.

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Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 4x? – 4x.…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 64x2 +…

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Q: Find the equation of the tangent line to the circle at the point (-3, -4). Equation of the circle *…

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Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

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 equations of all lines through the origin that are tangent to the curve y = x³ – 6x2 7x. -…

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Q: Find the equation of the tangent line to the circle x^2 +y^2 =1 13 at the point ( 1/2 , (√3)/2 )…

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Q: Find the equation of the tangents: y=x² + 6x² + 10x + 8 parallel x-y= 2. to the line А.…

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Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y =…

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Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

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: 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: Find an equation of the curve that passes through the point (1, −2), and has the given slope y′ =…

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Q: Find the equations of the tangent lines to the graph of y=x²+6 that go through the point (0,-2) and…

A: Given problem:- Find the equations of the tangent lines to the graph of y = x2 +6 through the point…

Q: Find equations of all lines having slope -1 that are tangent to the curve y = 1/(x - 1).

A: Given, y=1x-1 Slope,m=-1

Q: Find equations of all lines having slope −3 that are tangent to the curve y=3/(x−4)

A: Equations of all lines having slope −3 that are tangent to the curve y=3x-4

Q: Does the parabola y = 2x2 - 7x - 1 have a tangent whose slope is -1? If so, find the point of…

A: Recall: Slope , m= dydx Point - slope intercept form : (y-y1)=m(x-x1) ; where 'm' is the slope

Q: 1. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? a. -5 b. -6 C.-7…

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Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: The slope of the tangent line to the parabola y 3x + 3x +7 at the point (- 5, 67) is: The equation…

A: Take the derivative and put the given point.

Q: Determine the equation of the line tangent to y = /1+x³ at the point (2, 3).

A: The given function is y=1+x3. Its derivative is obtained as, dydx=ddx1+x3=121+x3ddx1+x3=3x221+x3 at…

Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 4x² – 4. -…

A: Topic:- application of derivatives

Q: 2) Find the slope and the equation of the tangent line to a curve: y = 3x? - 4x + 1 at x = 2.

A: The given curve is y=3x2-4x+1, we have to find slope and the equation of tangent line to the curve…

Q: Find equations of the tangent lines to the curve У 3 that are parallel to the line x - 2y = 5.…

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Q: Find the equation of the line that is tangent to the graph of y= x^3 +4/x^2 at point (2,9)

A: The equation of tangent line to y=f(x) at (x0,y0) is y-y0=f'(x0)(x-x0)