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

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Question 1010714: identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci
5x^2-5y^2+40x-20y+35=0
Click here to see answer by josgarithmetic(39618)

Question 1010717: identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci
y^2-3x+10y+37=0
Click here to see answer by stanbon(75887)

Question 1010890: I don't understand how to complete this problem: Write an equation for the parabola whose vertex is at (2,6) and which passes through (4,-1).
Click here to see answer by Boreal(15235)

Question 1010715: identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci
x^2+y^2-4x+6y=0
Click here to see answer by Boreal(15235)

Question 1010713: identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci
y^2-3x+10y+37=0
Click here to see answer by MathLover1(20850)

Question 1011162: write the equation of a hyperbola with vertices at (3,-1) and (3,-9) and co-vertices at (-6,-5) and (12,-5)
Click here to see answer by MathLover1(20850)

Question 1011293: the equation of a circle is given by x^2 + y^2 - 10x -8y + 25 = o
i. show that the circle touches the x-axis
ii. find the coordinates of the point of contact
Click here to see answer by josgarithmetic(39618)

Question 1011469: Find the equation of the locus of a point P (x,y) that follows the condition of:
P is sqroot (2) units from the line with equation y = x
Click here to see answer by josgarithmetic(39618)

Question 1011526: Find the equation of the locus of Point P (x,y) when:
(a) The distance of P from the y axis is 3 times greater than the distance from the x axis

Click here to see answer by ikleyn(52795)

Question 1010436: Analyse the equation 4x^2-4xy+y^2+5√5x+5=0 using rotation of axes
Click here to see answer by ikleyn(52795)

Question 1011590: Find the equation of the locus of a point p (x,y) when:
1. the distance of P from the line y=-5 is three quarters of its distance from the line x = 2
2. The distacne of P from the line x= -3 is two fifths of its distance from the line y= -1

Click here to see answer by josgarithmetic(39618)

Question 1011589: Find the equation of the locus when the distance of P from the line x=4 is equal to its distance from the line y = 1
Click here to see answer by ikleyn(52795)

Question 1011593: Find the equation of the locus when The distance of P from the line x= -3 is two fifths of its distance from the line y= -1
Click here to see answer by josgarithmetic(39618)

Question 1011617: Find the equation of the locus when:
The distance of P from the line x = -3 is two fifths of its distance from the line y = -1.
I do not have trouble solving it, but i want an explanation on how the slope is 5/2
Click here to see answer by ikleyn(52795)

Question 1011663: Can someone please help me. Graph each equation. Identify the conic section, any lines of symmetry, and the domain and range. X=2y^2+5

Click here to see answer by rothauserc(4718)

Question 1011619: Find the locus of a point P that moves so that PA^2 - PB^2 = 5
Click here to see answer by ikleyn(52795)

Question 1011854: A ladder that is 6m long rests with one end on the horizontal ground and its other end against a vertical wall. Considering the ground and the wall as the x and y axes respectively, find the locus of the possible midpoints of the ladder.
Click here to see answer by ikleyn(52795)

Question 1011856: I found the locus of a question to be x^2 - 16x +y^2 +4y +28 = 0.
I need help with this part: What point on the straight line joining the points (-4,2) and (5,-1) is on the locus.
Click here to see answer by Alan3354(69443)

Question 1011877: A is a point where the circle with equation x^2 +y^2 = 16 cuts the x axis. Find the locus of the midpoints of all chords of this circle that contain A.
I know that A can be (4,0) and (-4,0)
Click here to see answer by MathLover1(20850)

Question 1011969: The equation of the path of a cricket ball thrown at an angle of 45 degrees to the horizontal is y = x - x^2/50, where x and y are the horizontal distance travelled and the vertical height respectively. Calculate the greatest vertical height reached and the horizontal distance travelled.
What i have done so far:
y = x - x^2/50
50y = 50x - x^2
= -(x^2 - 50x) + 0
= - (x-25)^2 + 625
Therefore greatest height would be 625 divided by 50 which is 12.5, and that answer is correct.
But I don't know how to get horizontal distance???

Click here to see answer by macston(5194)

Question 1011968: A stone is thrown straight up from the ground. The height above the ground, h(t) metres is a function of time, t seconds (t >0) according to the rule h(t) = 20t - 5t^2. Find:
a. the domain of h
I do not understand how to acquire the domain of the function. Can you please explain how to get to the answer of 0 < t < 4
b. the greatest height achieved
I solved this part:
-5t^2 + 20t + 0
-5(t^2 - 4t) + 0
-5(t^2 - 4t + 4) + 20
-5( t - 2)^2 +20
So the maximum distance is 20

Click here to see answer by macston(5194)

Question 1012031: the orbit of mercury around the sun forms an ellipse with eccentricity 0.206,length of the major axis 1.16*10^8km and the sun at one focus. what is the aproximate distance from mercury to the sun?
Click here to see answer by ValorousDawn(53)

Question 1012211: draw the graph of the parabola y*y+4x=0 also findn it's focus and directrix?

Click here to see answer by josgarithmetic(39618)

Question 1010722: worlds of fun is designing a new ride the ride has 2 tracks that are hyperbolic if the ride is placed on a coordinate grid the vertices of the ride are at (-3,2) and (5,2) and the foci are at (-5,2) and (7,2)
explain how to find the values of A,B, and C for the hyperbolic tracks and state their values
Click here to see answer by FormerJosephStalin(2)

Question 1012349: solve:
(x + 3/x )^2 = 16
Click here to see answer by josgarithmetic(39618)

Question 1012362: gog=g(g(x))
Click here to see answer by Theo(13342)

Question 1012359: If you have 100*�-5*+3) pesos in your wallet and you spent (80*�-2*�+9) pesos in buying foods, how much money left in your packet?

Click here to see answer by Alan3354(69443)

Question 1012355: A vendor gained P (3*�+6*-4) on the first day and gained P (13*+8) on the 2nd day, Hhow much profit did the vendor gain in 2 days?

Click here to see answer by Alan3354(69443)

Question 1012461: A piece of wire 6 metres long is cut into 2 parts. One part is used to form a square and the other to make a rectangle whose length is 3 times its breadth. Find the lengths of the 2 parts if the sum of the two areas is a minimum.
Click here to see answer by ankor@dixie-net.com(22740)

Question 1012465: ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x.
Show that the area 'y' of the quadrilateral CDFE is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area.
Click here to see answer by ikleyn(52795)

Question 1012462: A large open area is to have a section surrounded by a rectangular fence. This rectangle is then divided into six smaller rectangles, using one dividing fence parallel to its length and two fences parallel to its breadth. If the total length of fencing available is 1200m, find the maximum possible area.
Click here to see answer by ankor@dixie-net.com(22740)

Question 1012464: A machine comes in 2 parts, which weigh 'x' kg and 'b' kg respectively. The cost 'c' of the machine is given by c = 2x + b. The earning capacity 'y' of the machine is given by y = x(x+b). If 'c' has the fixed value 10, express y as a function of x and hence find the value of x for which y is a maximum. Find the maximum value of y.
Click here to see answer by Theo(13342)

Question 1012602: ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x.
Show that the area 'y' of the quadrilateral CDEF is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area.
Click here to see answer by rothauserc(4718)

Question 1012925: given that x =2 is a root of the equation x^2 + x +m = 0, find the other root and the value of m

Click here to see answer by fractalier(6550)

Question 1013006: For what values of k will the equation have roots that are equal but opposite in sign
Click here to see answer by ikleyn(52795)

Question 1013006: For what values of k will the equation have roots that are equal but opposite in sign
Click here to see answer by Theo(13342)

Question 1013006: For what values of k will the equation have roots that are equal but opposite in sign
Click here to see answer by MathLover1(20850)

Question 1013457: a parabolic arch has a width of 18 m across the bottom. at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?
Click here to see answer by Alan3354(69443)

Question 1013652: Please help me find the equation of the asymptote of 3x^2-2y^2=6
Click here to see answer by Theo(13342)

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