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

Tutors Answer Your Questions about Quadratic-relations-and-conic-sections (FREE)

Question 869723: How do I write (x-1)^2+5(y+2)^2=20 (an ellipse) in standard form? I know you divide by 20, but would it be (x-1)^2/20 + 5(y+2)^2/20=1? Whats the answer?
Click here to see answer by josgarithmetic(39620)

Question 869725: write the equation of each circle
center (-3,7) and radius is 12
please help
Click here to see answer by jim_thompson5910(35256)

Question 869742: Okay well I have broken down the equation of
Y=-5x^2+30x-36
Down to
Y=-5(x^2-6x)-36
I'm trying to break it down to standard form.
Then it's telling me to recall that be constant term in a perfect square is the square of half of the coefficient of the linear term therefore 9 is added inside the parentheses to form a perfect square
Leaving x^2-6x+9
My question is where exactly did the 9 come from?
Click here to see answer by mananth(16946)

Question 869735: Supposedly this is a hyperbola:

rearranging the terms and completing the squares:

Simplifying into "standard form":

But hyperbola in standard form should equal 1
What kind of shape is this equation?
Click here to see answer by josgarithmetic(39620)

Question 869730: write the equation of the circle
center (4,-2)
containing the point (-4,13)

can someone explain please

Click here to see answer by josgarithmetic(39620)

Question 869730: write the equation of the circle
center (4,-2)
containing the point (-4,13)

can someone explain please

Click here to see answer by MathTherapy(10552)

Question 869728: How do I write the equation of the circle if its endpoints of the diameter are at (3,4) and (-5,0)?
Click here to see answer by josgarithmetic(39620)

Question 869746: How do I write the equation of the circle if its endpoints of the diameter are at (3,4) and (-5,0)? Thanks.
Click here to see answer by josgarithmetic(39620)

Question 869869: Find the center, vertices, and foci of the hyperbola. Graph the hyperbola.
(Y+2)^2/9-(x-1)^2/16=1
Click here to see answer by ewatrrr(24785)

Question 869877: How do I write the equation for the circle (2,5) with a radius of 4

Click here to see answer by Fombitz(32388)

Question 869883: Graph 𝑥^2+𝑦^2=(𝑥^2+𝑦^2−𝑥)^2. This is from the conics rotation of axes section.
I understand the hyperbola and ellipse section. But I could really use some insight on this. THANKS TO ALL
Click here to see answer by Fombitz(32388)

Question 869891: Solve the equation z^3-1=i
This is from the Pre- CAlculus Conics Rotation of Axes section. I am just stumped on a couple problems
Click here to see answer by Alan3354(69443)

Question 869893: Graph 𝑥^2+𝑦^2=(𝑥^2+𝑦^2−𝑥)^2
This is from the Pre-cal conics Rotation of Axes section.
I understood the elipsee and hyperbola section just stumped on these last questions.

Click here to see answer by Fombitz(32388)

Question 869892: Determine the eccentricity of:

Click here to see answer by ewatrrr(24785)

Question 869890: Let (ax+b)/(x^2-1)=a/(x+1)+b/(x-1). Find a and b.
This is from the Pre-Cal Conics, rotation of axes section. Any help would be awesome. thank you
Click here to see answer by josgarithmetic(39620)

Question 869933: rotation of Axes Question(PRE-CAL) 32x^2-48xy+18y^2-15x-20y=0
A. rewrite the equation in a rotated x^1y^1 system w/o an x^1y^1 term. USe the appropriate rotation formulas
B express the equation involving x^1 and y^1 in the standard form of conics section
C Use the rotated system to graph the equation

Click here to see answer by stanbon(75887)

Question 869968: What is the equation of the ellipse with co-vertices (-20, 0), (20, 0) and foci (0, -8), (0, 8)
Click here to see answer by josgarithmetic(39620)

Question 870110: Find an equation for the hyperbola and Satisfies the given conditions.
Foci(+-5,0), vertices (+-3,0)
Please help. Super confused.
Click here to see answer by josgarithmetic(39620)

Question 870212: The ellipse with one focus at (2,5) and minor vertices at (-1,7) and (-1,3)
Graph the conic and find its equation in standard form
Click here to see answer by josgarithmetic(39620)

Question 870069: find the x-intercept for the parabola defined by this equation y=4x^2-9x+5
Click here to see answer by lwsshak3(11628)

Question 868923: You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 ft. above you. The height of the grappling hook you throw is given by the function h(t) = -16t^2 - 32t + 5.
What is the maximum height of the grappling hook? Can you throw it high enough to reach the ledge?
Click here to see answer by lwsshak3(11628)

Question 868052: Find the equation of a hyperbola with foci (-6,0) and (4,0) and a vertex at (-5,0).
Click here to see answer by lwsshak3(11628)

Question 868741: Write an equation of each ellipse with the given characteristics in standard form.
Foci (5,0), (-5,0)
Co vertices (0,2), 0,-2)
Click here to see answer by lwsshak3(11628)

Question 870398: How to find the axis of symmetry for m^2-5m-14=0
Click here to see answer by Alan3354(69443)

Question 870428: What is the equation, in standard form, of the parabola with focus (3,0) and directrix x = -3?
Click here to see answer by ewatrrr(24785)

Question 870460: write the equation of this circle
the equation of the line tangent
x^2+y^2=225 at (9,-12)
please help
Click here to see answer by josgarithmetic(39620)

Question 870622: Find the equation of the parabola with focus F(4,0) and directrix x=3 by using the Distance formula
Click here to see answer by josgarithmetic(39620)

Question 870681: how to make 5y^2- 4x^2 = 20 into a vertex from and identify the type of conic section and its direction?
Click here to see answer by ewatrrr(24785)

Question 870783: Please help....I cannot help my son with this question.
What is the equation of the quadratic graph with a focus of (6,0) and a directrix of y=-10?
Please explain, if possible how to work this kind of a problem. Thank you so much!!!
Click here to see answer by josgarithmetic(39620)

Question 870811: 14. Write an equation of a parabola with vertex at the origin and the given focus. (0,6)
Click here to see answer by ewatrrr(24785)

Question 870814: 18. Write an equation of a parabola with the given focus and directrix. Focus-(0,3), Directrix- y=-1
Click here to see answer by ewatrrr(24785)

Question 870824: (y-1)^2/45 - (x+2)^2/36=1
Click here to see answer by ewatrrr(24785)

Question 870819: y^2=-4y+2x+1
1. how do you write in standard form
2. and what will the graph look like

Click here to see answer by ewatrrr(24785)

Question 870922: Use the Distance Formula to find the equation of a parabola with the focus F(4,0) and directrix x=-3.

Click here to see answer by lwsshak3(11628)

Question 870991: (y+1)^2=-8(x+3)
Click here to see answer by lwsshak3(11628)

Question 871001: Put in standard form and identify the conic
1) y^2-x^2+6x-4y=6
2)x^2+y^2+14y=-13
3) 4x^2+9y^2+16x-54y=-61
4) x^2+4y^2-2x-15=0
I'm very confused any help would be very appreciated
Click here to see answer by richwmiller(17219)

Question 871005: 4x^2-y^2+8x+2y=13
Click here to see answer by josgarithmetic(39620)

Question 870918: Write an equation in standard form for the hyperbola with center (0,0) , vertex (0,6) , and focus (0,8).
*I tried actually graphing it but it was no use. I also tried b squared minus 4 multiplied by a and c.
Click here to see answer by lwsshak3(11628)

Question 871184: Find the roots/zeros/x-intercepts of m^2-5m-14=0
Solve by factoring.
Click here to see answer by Fombitz(32388)

Question 871179: Find the y intercept of the quadratic equation m^2-5m-14=0
Click here to see answer by Fombitz(32388)

Question 871205: Translate the equation three units right and 5 units up. Write the new equation
1) 9x^2+3x+10=16y^2+154+3x
2)x^2+4y^2+6x-7=0
3)x^2-y^2+6x+10y=17
Click here to see answer by ewatrrr(24785)

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