For the ellipse b'x' + a'y a'b?, show that the equations of its tangents of slope m

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: 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: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

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Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

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

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Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

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

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Q: Draw a diagram to show that there are two tangent lines to the parabola y = x 2   that pass through…

A: Explanation: Given that,                     Assume that, point of tangency is (a, a2). Slope of…

Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

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Q: Find the slope of the tangent line to the ellipse 1 at the point 25 slope =

A: Here the equation of ellipse is x29+y225=1 and the point is (m,n)We have to find the equation of…

Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

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 the point Q that is on the curve nearest %3D the point (4, 1)

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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 length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

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Q: How do I find the equation of the tangent line for this ellipse at the point (5/2,1). (x-1)^2/9  +…

A: Follow the steps.

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

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Q: A baseball is launched into the outfield on a parabolictrajectory given by y = 0.01x(200 - x). Find…

A: Given ------(1)   The average value of a functionon an interval is given by ------ (2) From the…

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find equations of both the tangent lines to the ellipse x2 +4y2 =36that pass through the point (12,…

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Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

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: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

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 slopes of the tangent lines to the ellipse 4x +y = 40 at y=2. The smaller slope is 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: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

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Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

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: 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 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 equations of both the tangent lines to the ellipse x + 9y2 81 that pass through the point (27,…

A: Given information: The equation of the ellipse is x2+9y2=81. Calculation: We need to find the…

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: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

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Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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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…

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Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

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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 tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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