Given the equation of a parabola as 12(y-5)=(x+3)^2, determine the following: Direction of opening: Answer( left, right, up or down)   The coordinates of the vertex. Answer as an ordered pair: (h,k)   The coordinates of the focus. Answer as an ordered pair: (x,y)   The equation of the directrix. Answer in the given format: y=b

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: 3x2-2y2+6x-8y=6⇒3x2+6x-2y2+8y=6⇒3x2+2x-2y2+4y=6⇒3x2+2x+1-2y2+4y+4=6+3-8⇒3x+12-2y+22=1⇒x+1213-y+2212=…

Q: center: (7,-2) focus: (10,-2) vertex: (9,-2) what is the standard form of the equation of this…

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Q: Graph the equation. Identify the focus and directrix of the parabola. y² =

A: y2=−4xcompare with y2=−4ax

Q: Solve the problem. A homeowner wants to make an elliptical rug from a 30-foot by 10-foot rectangular…

A: To solve this problem, we can use the fact that an ellipse can be defined by its semi-major axis…

Q: menE C. Find the center and the radius of the following equation: 5. x + y -16x+8y+31=0 6. x* +y…

A: Given equation of circle now we have to find centre and radius of circle as shown below

Q: F) Consider the parabola -18(y+10) = (x+8)*. Answer parts a-e. a) Which direction will the parabola…

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Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

Q: Put the equation that is in general form: �=�2-8�+15into standard vertex form: �=(�-ℎ)2+�:

A: The objective of this question is to convert the given quadratic equation from general form to…

Q: Write the given equation in the form y = a(x – h)² + k and identify the vertex, focus, directrix.…

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Q: The Gymnasium in Colegio de San Juan de Letran, Manila. is a whispering chamber. Its dimensions are…

A: Given : Dimensions are 56 feet wide by 106 feet long center is at (0,0) Draw an ellipse with center…

Q: For 7x - 4y-11=0, (a) Write the equation of the hyperbola in standard form. (b) Identify the center,…

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Q: For the equation of the parabola (x+2) = - 16(y-4), find: a) the vertex b) the focus c) the…

A: Compare the given equation with standard equation

Q: Graph the Ellipse and label the intercepts y = 5(x+3)²-3

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: 1. x²-2x-24y+1=0 Standard Form Equation: a. Vertex: b. Focus: C. Length of LR: d. Directrix:

A: Topic = Parabola As per guidelines , At a time only one question with three sub-parts can be…