Questions on Algebra: Conic sections - ellipse, parabola, hyperbola answered by real tutors!

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Question 620450: The filament of a light bulb is a thin wire that glows when electricity passes through it. The filament of a car headlight is at the focus of a parabolic reflector, which sends light out in a straight beam. Given that the filament is 2 inches from the vertex, find an equation for the cross-section of the reflector. If the reflector 6 inches wide, how deep is it?

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Question 620455: Find the center of the ellipse 4x2 + 9y2 - 40x - 54y + 145 = 0.
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Question 620459: Find the vertex of y = x2 + 5x + 4

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Question 620563:
A.Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
2x2 – 7y2 + x – y – 2 = 0
B.Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
8x2 – 4y2 – 4x – y + 8 = 0

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Question 620711: Let f (x) = x to the power of 2 + 3x -3
find f (-4) ; f (-1) ; f(-2x)
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Question 620706: Write the equation in standard form of a hyperbola with vertices at (-2,4) and (-2,6) and asymptote y=1/2x + 2
Click here to see answer by lynnlo(4164)

Question 620834: determine the shape of the graph represented by this equation: x^2+4y^2+12x-32y+96=0
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Question 620936: Identify the conic section. If it is a parabola, give the vertex. If it is an ellipse or hyperbola, give the center and the foci.

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Question 620924: An architectural engineer is designing a parabolic dome that will be 200 feet in diameter with a maximum height of 50 feet. Find the equation of the cross-sectional parabola of the dome.
Click here to see answer by ankor@dixie-net.com(15667)

Question 621036: What are the coordinates of the vertex and foci, and what is the equation for the directrix of the following parabolic equations?
a.
b.
c.
d.
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Question 620844: Help stuck again. I have an hyperbola with the formula of 36x^2+144x+27-9y^2+36y=0 I need to find the formula plus the asymtopes foci and vertices.
I make the formula out to be [(2/5)(x+2)^2]-(1/10)(y+2)^2 =1.
Click here to see answer by lwsshak3(6527)

Question 621020: y^2-x^2/15=1
Want to know the focus,vertices and the asymptote
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Question 621019: y^2-x^2/15=1
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Question 621143: Identify the conic section. If it is a parabola, give the vertex. If it is an ellipse or a hyperbola, give the center and the foci.

Click here to see answer by ewatrrr(10682)

Question 619584: Hi, please help me solve the question:
A rectangular sheet of steel is twice a long as it is wide. From each corner a 2 cm-square is cut. Then the sides are folded to make a box (without top), which holds 60 cubic centimeters. What were the original dimensions of the steel sheet?
Thank you!
Click here to see answer by lwsshak3(6527)

Question 621557: An arch can be modelled by the function: h=0.06d^2+2.13.
At a horizontal distance of 2 m from one end of the arch, how high is the arch, to the nearest tenth of a metre?
Click here to see answer by nerdybill(6963)

Question 621750: i need to find the standard form of this equation and the properties of the hyperbola , i would really appreciate this help
Click here to see answer by ewatrrr(10682)

Question 621554: Find the x intercepts of the parabola with vertex (1,-13) and y intercept (0.-11)
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Question 622202: Graph an ellipse with foci at (0, ±2 times square root of 10 ) and x-intercept at (9, 0).
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Question 621536: (x^2)/(4)+(y^2)/(16)=1
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Question 622704: Graph (x+1)^2/9 + (y+3)^2/25 = 1
Click here to see answer by ewatrrr(10682)

Question 622709: I am stuck on this parabola question can someone please help me list steps please.

The parabola given by the equation y=3x^2-30 x+28 has its vertex at (h,k) for:
h=
and
k=
Click here to see answer by ewatrrr(10682)

Question 622715: where is the transverse axis for this hyperbola?
8y^2-5x^2=40
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Question 622707: Parabola questions are the hardest can someone help me figure this out show steps please.

The parabola given by the equation y=-x^2+8 x-8 has its vertex at (h,k) for:
h=
and
k=
Click here to see answer by ewatrrr(10682)

Question 622703: I need help with this parabola question it is hard for me to find the vertex of this question.

Find the vertex of the parabola y = 12 x + 4 - x^2. Enter your answer as a point (h,k), including the parentheses.
The vertex is at the point:
Click here to see answer by ewatrrr(10682)

Question 622940: A quadratic equation f(x)=0 has a solution x= -1. Its graph has vertex at (3,4).What is the other solution?
Click here to see answer by richard1234(5390)

Question 623081: How do I graph a parabola X=(1/24)*y^2
Click here to see answer by Earlsdon(6290)

Question 623383: Graph the parabola.
y=-1/2x^2-x-9/2
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Question 623500: If the foci for an ellipse is (0,-1) and (0,1) and the major axis is 6, then is the ellipse horizontal or vertical? What would the equation of the ellipse look like?
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Question 623676: What is the length of the minor axis of the ellipse given by the equation x^2/144 + y^2/25 = 1?
Click here to see answer by ewatrrr(10682)

Question 623675: What are the vertices of the ellipse given by the equation x2 + 4y2 + 10x – 56y + 205 = 0?
?
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Question 623675: What are the vertices of the ellipse given by the equation x2 + 4y2 + 10x – 56y + 205 = 0?
?
Click here to see answer by math-vortex(472)

Question 623488: What is the standard form of the hyperbola with foci at (±4,0) and vertices at (±3,0)?
Click here to see answer by lwsshak3(6527)

Question 623928: I need someone help i am stuck doing this last part of my homework. can someone explain it to me

Match each equation for a parabola with the direction that the parabola opens.
1. y=-3(x+1)^2-8
2. x=-3(y+1)^2-8
3. y=3(x+1)^2-8
4. x=3(y+1)^2-8
A. up
B. right
C. down
D. left

Click here to see answer by ewatrrr(10682)

Question 623931: I just started doing parabola and circles i need some help. i need to find what A and B= to.

Find an equation for the ellipse whose graph goes through the points (9,0) and (0,2).
If your answer is \frac{x^2}{A}+\frac{y^2}{B}=1, then
Click here to see answer by ewatrrr(10682)

Question 623929: I need help with this circle problem it annoying me at this point can someone explain what i need to do in steps. Also need to identify H,K,R

Find the equation of the circle whose diameter has endpoints (-9, -2) and (1, 1). Write it in the form
(x-h)^2 + (y-k)^2 = r^2
Click here to see answer by ewatrrr(10682)

Question 623930: I need help in finding what H, K , R. Also finding the center of the circle.

Find the center (h, k) and the radius r of the circle
4 x^2 - 7 x+ 4 y^2 - 8 = 0 .
Click here to see answer by jsmallt9(3296)

Question 623803: The equations of three distinct circles are listed below. Using complete sentences, explain which of the three circles would intersect the x-axis only. Justify your answer.
Circle A: (x – 9)2 + (y – 3)2 = 25
Circle B: (x –7)2 + (y + 2)2 = 49
Circle C: (x + 2)2 + y2 = 16
Click here to see answer by jsmallt9(3296)

Question 623946: can you write y = -3x^2 - 18x - 29 in vertex form
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Question 623945: what is the vertex and the y intercept of the graph function y = 2(x + 2)^2 - 2
Click here to see answer by ewatrrr(10682)

Question 623962: how do i plug into the pythagoreaum theorum with an ellipse?

Click here to see answer by solver91311(16897)

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