Consider the parabola y 7x-x. Find the slope of the tangent line to the parabola at the point (1, 6). (b) Find an equation of the tangent line in part (a) (c) Graph the parabola and the tangent line. 20 20 마 10 10 20 10 20 -20 10 20 10 0 20 10 10 10 10 20 10 20 -20 -20 -10 -20 Talk to Tutor

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: Find an equation for parabola with vertex  (−1,3) and directrix x=−4.

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Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: How can we find the slope of the parabola y?

A: You can’t find the slope of the parabola y , because a parabola is not a line. You can find the…

Q: 2)Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

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Q: write an equation showing the family of curves with the given parameters: 1. Family of parabolas…

A: To find the equation showing the family of curves of parabolas with axis parallel to the x-axis

Q: What is the families of the curve of all Parabolas with symmetric axis parallel to the y-axis and…

A: Given: What is the families of the curve of all Parabolas with symmetric axis parallel to the y-axis…

Q: Determine the equation in standard form of the parabola that satisfies the given conditions…

A: Given that :

Q: Write the equation for the hyperbola with foci (1,-5), (9.-5) and conjugate axis of length 6. (x-…

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Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F1 (0, 0) and F2 (0, 4)V

A: Consider the given information. y−k2a2−x−h2b2=1 Since we have the given foci at F1(0,0) and F2(0,4).…

Q: Find the standard form of the equation of the parabola with the given characteristics. vertex: (2,4)…

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Q: The vertical line passing through the vertex of a parabola is called the ......... .

A: Given The vertical line passing through the vertex of a parabola is called the ......... .

Q: A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always…

A: The given parabolic curve is, y2 = 8x    ...(1)   It is given that the rate of change of ordinate is…

Q: 5. The equation of a family of parabolas with axis paralel to the y-axis is

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Q: find the equation of the tangent line through the point (2,-2) to the hyperbola x2-y2=16.

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Q: 4. The equation of a family of circles with center an the y-axis is 5. The equation of a family of…

A: Topic:- geometry  Note:- as per our guideline if more than one question uploaded than only first…

Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

Q: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

Q: Find an equation of the parabola with vertex (3, 4) and directrix y = 1.

A: Graph of parabola :

Q: Find the equation of the line normal to the parabola y = x2 - 6x + 12 perpendicular to the line that…

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Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: We have Vertex=(0,0)Directrix x=-15

Q: Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-3, -12)…

A: Given-  To graph- The parabola and tangent line which is passing through -3,-12.

Q: 1. What is the equation of the line to the parabola y = x2 + 5x +1 through the 15 point at

A: Given, Parabola  y=x2+5x+1 Point 12, 154

Q: Find the equation of a parabola that has a vertex of (7, -4) and contains the point (0, 94),…

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Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: Find the slope of the line tangent to the conic section 25 (х-2)2 (y-6)2 = 1 at (2,10). 16

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Q: 2 What are the intersection points of the parabola given by the equation y = x“ – 9 and the line…

A: We are answering only the first question as per our honor code. Given, The equation of a parabola…

Q: How do you find the standard form of the equation of the parabola with the given characteristic(s)…

A: Given vertex is at origin i.e (h,k) = (0,0) To find the standard equation of parabola

Q: Find the standard form of the equation of the parabola with the given characteristic and vertex at…

A: equation of parabola  (x - h)2 = 4p (y - k) where (h,k)=(0,0) vertex ordinates directrix y=3 , y= k…

Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

A: We have to determine the equation of the parabola whose vertex is at the point (-1,-1) and whose…

Q: a) Find the equation of the tangent line to the parabola at the given point. y = −4x2,  (3, −36)…

A: Given: a) y = −4x2,  (3, −36)   To find: The equation of the tangent line to the parabola at the…

Q: 2) WHAT ARE THE STANDARD EQUATIONS OFA HYPERBOLA WITH A HORIZONTAL TRANSVERSE AXIS AND OF A…

A: Solution is given as below:

Q: What are the intersection points of the parabola given by the equation y = x2 – 9 and the line given…

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Q: How can we Find the slope of the parabola?

A: Let the equation of a parabola be: y^2 = 4ax

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: Find the equation of a parabola that has a vertex of (2, -4) and contains the point (1, -7).…

A: Given  Vertex of parabola (2,-4)  And contains the points (1,-7)

Q: Find the equation of the parabola that is symmetric about y axis with vertex at the origin and…

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Q: 4. What is the family of curves for all parabolas with axes parallel to the y-axis. Add File

A: We will find out the required solution.

Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F, (0, 0) and F2 (0, 4).

A: Since, the foci of the given hyperbola are F′(0,0​) and F(0,4​) which lie on the X-axis and…

Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)