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

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Question 1142988: The orbit of Earth around the sun is in the shape of an ellipse where the sun is at one of the foci, and whose length of the major axis is 185.8 million miles. If the distance of the sun from the center of the orbit is 1.58 million miles, find the least and greatest distance of Earth from the sun.
Click here to see answer by rothauserc(4718)

Question 1143057: Write the equation of the parabola in standard form and determine its vertex, focus, directrix, and axis.
2
y +4x -8y +28=0
Click here to see answer by greenestamps(13200)

Question 1143056: Write the equation of the parabola that has the given charcteristics.
Vertex(3,-2) directris x=-5
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Question 1142918: the bulb is placed 6cm from the vertex and the depth of the headlight is 12cm. Find the diameter of the headlight at its opening
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Question 1143338: (y+4)²=16(x+2)
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Question 1143601: A tunnel has the shape of semi ellipse that is 15 ft. high at the center, and 36 ft. across at the base. At most how high should a passing truck be, if it is 12 ft. wide, for it to be able to fit through the tunnel? Round off your answer to two decimal places.
Click here to see answer by Alan3354(69443)

Question 1143600: The foci of an ellipse are (-3,-6) and (-3,2). For any point on the ellipse, the sum of its distances from the foci is 14. Find the standard equation of the ellipse.
Click here to see answer by greenestamps(13200)

Question 1143657: Find the equation of the circle that passes through the points of intersection of the circles x²+y²=2x, x²+y²=2y and has its center on the line y=2.
Click here to see answer by ikleyn(52795)

Question 1143668: Passes through the points of intersection of the circles x²+y²+2x-4x+6y=12, x²+y²+4x-8y=28 and has its center on the y axis.

Click here to see answer by Alan3354(69443)

Question 1143668: Passes through the points of intersection of the circles x²+y²+2x-4x+6y=12, x²+y²+4x-8y=28 and has its center on the y axis.

Click here to see answer by ikleyn(52795)

Question 1143684: 1.Vertices
(1,7) and (1,-3); a minor axis of lenght 4
2.Center at(-2,3); major axis is horizontal;passing through (1,4)and (2,3)
3.Vertices at (-1,1) and (-1,-5); passing through the origin
4.Center at the origin; focus at (2,0); vertex at (0, 3)
Click here to see answer by Alan3354(69443)

Question 1143683: Sketch ellipse with the given rquation. Clearly indicate center,vertices,focia and the endpoints of the minor axis
4x²+8y²-12y+16y+1=0
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Question 1143730: Determine the equation of the circle inscribed in a triangle, if the triangle has its sides on the lines y=0, 4x+3y-50=0, and 3x-4y=0. Sketch the graph.
Click here to see answer by ikleyn(52795)

Question 1143729: Find the equation of the circle inscribed in a triangle, if the triangle has its sides on the lines 2x+y-8=0, x-7y-19=0, and x-y-1=0. Sketch the graph.
Click here to see answer by ikleyn(52795)

Question 1143755: Determine the lines tangent to the circle x^2+y^2-2x-8y+15=0 and x-y+10=0. Sketch the graph
Click here to see answer by Alan3354(69443)

Question 1143755: Determine the lines tangent to the circle x^2+y^2-2x-8y+15=0 and x-y+10=0. Sketch the graph
Click here to see answer by ikleyn(52795)

Question 1143793: what the slope of the tangent line of the curve x^2-xy+y^2=3 at a point (1,2)
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Question 1143792: find the equation of the circle woth center at (-3,8) and tangent to the line
x-y+5=0

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Question 1143791: find the area enclosed by the curve x^2+y^2-3x-8y+18=0
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Question 1143790: find the area bounded by y^2=4x and y+2x=12
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Question 1143812: find the vertex of the parabola whose equation is y²+3x-2y+7=0
Click here to see answer by greenestamps(13200)

Question 1143813: Given the points A(1,5), B(5,-2) C(-5,-5) and D(-15,1).
1.Find the area of the quadrilateral ABCD. Hint:divide the area into two triangles.
2.find the equation of a line AB?
Click here to see answer by Alan3354(69443)

Question 1143788: find the area bounded by y=6x-2x^3 and the line y-4=0
Click here to see answer by ikleyn(52795)

Question 1143788: find the area bounded by y=6x-2x^3 and the line y-4=0
Click here to see answer by greenestamps(13200)

Question 1143867: In a bridge that is upward how do I find all the parts with only given the height and length of a bridge which is the height is 377 and the length is 3600
Click here to see answer by ikleyn(52795)

Question 1143861: The light bulb of a parabolic reflector is placed at the focus of the reflector for better reflection. Suppose that the reflector is 18 inches and 10 inches deep. What is the equation of the parabola in the parabolic reflector?

Click here to see answer by Alan3354(69443)

Question 1143991: Find a set of parametric equations for the conic section or line below;
Ellipse: Center: (5,-3); Vertices: 6 units above and below the center; Endpoint of minor Axis: 2 units left and right of center.
A. x=5+6cos t, y=-3+2 sin t
B. x=5-2cos t, y=-3-6 sin t
C. x=5+2cos t, y=-3+6 sin t
D. x=2+5cos t, y=6-3 sin t
Click here to see answer by greenestamps(13200)

Question 1143998: The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tower is 295 feet. The smallest diameter of the tower is 166 feet which is 407 feet above the ground. The tower is 524 feet tall.
Find the width of the tower at a height of 233 feet.

Click here to see answer by greenestamps(13200)

Question 1143997: The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom tower is 285 feet. The smallest diameter of the rower is 156 feet which is 422.5 feet above the ground. The tower is 573 feet tall
Find the width of the tower at a height of 40 feet
Click here to see answer by greenestamps(13200)

Question 1144010: Find the equation of the parabola with the following properties
Focus at (1,-4)
Directrix is the x-axis

Click here to see answer by josgarithmetic(39618)

Question 1144028: Hi, i just need some help. Find the values of the constant k so that the graph of x^2+y^2+6x-4y=k^2-k-33 is a.) a circle, b.) a single point and c.) an empty set. I found a same problem but i need a whole solution thank you very much
Click here to see answer by MathLover1(20850)

Question 1144013: Find the equation of the hyperbola with the following properties.
Foci at (10,1) and (10,11)

Asymptotes of y-6 = ± 3/4(x-10)

Click here to see answer by greenestamps(13200)

Question 1144012: Find the equation of the hyperbola with the following properties.
Foci at (-8,-7) and (-8,-13)
Vertices at (-8,-9) and (-8,-11)

Click here to see answer by greenestamps(13200)

Question 1144011: Find the equation of the hyperbola with the following properties.
Foci at (5,-4) and (13,-4)
Vertices at (6,-4) and (12,-4)

Click here to see answer by greenestamps(13200)

Question 1144230: Find the general form of the equation of the ellipse with center at (2,3), vertices at (2,-1) and (2,-5), foci at (2,-3+√3) and (2-3-√3)
Click here to see answer by ikleyn(52795)

Question 1144229: Determine the standard form of the equation of the ellipse with center at (-4,7), a focus at (-4,11), and a vertex at (-4,12).
Click here to see answer by Edwin McCravy(20056)

Question 1144228: Determine the general equation of the ellipse with center (0,0), a focus of (0, √7), and a vertex of (0,4).
Click here to see answer by greenestamps(13200)

Question 1144228: Determine the general equation of the ellipse with center (0,0), a focus of (0, √7), and a vertex of (0,4).
Click here to see answer by ikleyn(52795)

Question 1144268: Find an equation of the line containing the centers of the two circles.
X^2+y^2+6x+4y+12=0
X^2+y^2-2x+10y+22=0
Click here to see answer by greenestamps(13200)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955