1. Find two possible equations for a parabola with a vertex V(0,3) that passes through the point P(4,6). The axis of symmetry of each parabola is parallel to a coordinate axis. a. What is the equation of the parabola whose axis of symmetry is parallel to the y-axis? b. What is the equation of the parabola whose axis of symmetry is parallel to the x-axis? 2. Use the law of cosines to solve that SAS triangle. b=5, c=11, A=30- 3. Find the vertex, focus and directrix of the parabola: (y-7)2-6(x+9) Use a calculator to find values of y in degrees. 4. a. sin (.62) b. csc '(7.89) c. tan (12) 5. Find a set of parametric equations for the rectangular equation b. y-9x+1 a. y=2x +6 6. Find the trig values using reference angles. 33m, b. csc() 7. Find the standard form of the equation for the ellipse centered at (0,0), having vertical major a. cos 270• axis of length 72 and minor axis of length 24 8. Use Heron's Formula to find the area of the triangle. a=10, b3D3, c=8 9. Convert points between polar and rectangular form. b. (3, 3) 10. Solve the ASA triangle where A=44•, b= 8 ft and C=57 a. (4,135-) 11. Use the trig identities to solve the equation in the interval (0.2) (Hint: find solutions for n-01

Q: 14. Which equation represents the given parabola? O y = -4(x – 4)² + 5 O y = }(x – 4)² + 5 O y =…

A: First option is correct.

Q: Which of the following equations is the equation of tangent to the parabola y2 = 2x + 8 at point…

A: The given equation of parabola is: y2=2x+8

Q: The following hyperbolas are confocal: x2/4 –y2/8 =1 and x2/6 –y2/k =1. What is the value of k

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = -8 in standard form?…

A: Given that, vertex of parabola is (h, k) = (0, 0) diretrix of parabola is, y = -8 We have to find…

Q: 16. The standard form of the parabola is (y – 5)² = 12(x + 3). Solve the following. a. Vertex b.…

A: a) vertex If the equation of parabola is (y-h)2=4p(x-k) the vertex is (k,h) for the given equation,…

Q: Let P and Q be distinct points on the parabola y = 2r such that a circle with PQ as diameter passes…

A: The given equation of parabola y2=2x Let P and Q be points on the parabola  Parametric coordinates…

Q: 5. Find the vert ex, focus, and directrix of the parabola y? + 6y + 2x +1 = 0 and sketch its graph.

A: The given parabola equation is  y2 + 6y + 2x + 1 = 0 To find  vertex, focus and directrix of given…

Q: The graphs of the conics intersect at two points. x² + y? = 9 = 1 4 What are the coordinates of…

A: To find the points of intersection ,first we find y2 from the two given equations and by  equating…

Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

Q: 10. Which is the equation of a hyperbola with co-vertices at (0, 7) and (0,-7) and a transverse axis…

A:

Q: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given the focus of parabola is -3,5 and directrix is y=-1.

Q: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: 1. Use the focus-directrix definition of a parabola to answer the following questions. 1) How would…

A: (1) When the focus is moved up the parabola opens wider, in other words as the parabola gets…

Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

A:

Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

A:

Q: Find three points on the parabola. x^2−8x−8y−8=0

A:

Q: Two stations that are 2 km apart receive a sound signal issued from a source located at point…

A: The distance between the point 0,-1 and the point P (x, y) is, d1=x2+y+12 The distance between the…

Q: 14. Find an equation for the parabola with directrix at r= -1 and focus (5, 1).

A:

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

A:

Q: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix x…

A:

Q: The parabola y = ax? + k has vertex (0, –1) and passes through the point (4, 2). Find its equation.

A: we have to find the equation of parabola

Q: 8: Which one of the following conics is a parabola? 22 + y + 5 = 4æ B 222 + y? = 4x +4 4r – 9y? +…

A:

Q: Find the equation of the parabola if vertex at (1,-1) the axis of symmetry is parallel to y-axis and…

A: Equation of parabola that have an axis of symmetry parallel to y-axis and the vertex at h,k is…

Q: (--2) 17 – 2 4 Find the equation for the parabola that has its focus at the and has directrix at x =…

A:

Q: 5. What is the standard for equation of a parabola with its vertex at (0,0) and a directrix of x-3?…

A: Given: A parabola has vertex 0, 0 and directrix x=3      ……1   To find: Equation of parabola

Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

A:

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Given :

Q: 11. Which of the following is the standard form of the equation of a parabola with a horizontal axis…

A: 11.    Standard form of the equation of a parabola with a horizontal axis of symmetry is given by:-

Q: Find the directrix of the parabola described by the equation 6 (x – 3) + (y + 2)? = 0 O x = } O x =…

A: The  parabola with vertex at (h,k) and focus at (h-a,k) has a standard equation, (y-k)2=-4a(x-h) The…

Q: Experiment #1: While bouncing the Infinity Ball, Nikki notices that the trajectory of the ball is in…

A: Given: Nikki notices that the trajectory of the ball is in the shape of parabola. She compares the…

Q: 22. Which of the following is the equation for a parabola with a vertex of (3, 1) and a focus of (3,…

A:

Q: Find the eccentricity of a hyperbola whose transverse axis and conjugate axis are equal in length O…

A:

Q: Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−254

A: Focus of the parabola is -394, -4 and directrix is x=-254. Now, Focus=-394, -4⇒h+p, k=-394,…

Q: 1. Consider the parabola whose directrix is at x = -7 and whose focus is at (-1, 1). What is the…

A:

Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

Q: What is the equation of the given parabola? y 4 -5-4-3-2 1 2 3 4 5 A y= 3x² 6x +3 I23 45

A: Here zeros form equation y=a(x-p)(x-q) p,q are zeros of equation

Q: 3. Find an equation of a parabola with a vertex at the origin and directrix y=-3.5 Oy=--x 14 Oy= ?…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

A:

Q: A parabola has a vèrtex at the origin and a focus of (0, 3/2). What is the equation of the parabola.

A: The general equation of a parabola with vertex at origin is given by y2=4ax. The distance between…

Q: 2 The parabola y = x + 9 has two tangents which pass through the point (0, – 6). One is tangent to…

A:

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

A:

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A:

Q: Consider the following equation of a parabola.Find three points on the parabola. (y−8)^2=−7(x−5)

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Q: 1) Find the intercept(s) and vert ex of the parabola. y=x^2-1

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Q: 4) Find the equation of a parabola which has the focus at (2,9) and the directrix at x=10.

A:

Q: 12. Determine the equation of the directrix for the parabola 20x=y2–10y+30 а. X-20 b. y=-20 с. X3-20…

A: Question : Determine the equation of the directrix for the parabola 20x = y^2 - 10y +30.

Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

A:

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at r %3D 24…

A: