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

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Question 1132758: The circle x^2 + (y-c)^2=r^2, where c >0 and r>0, lies inside the parabola y=x^2. The circle touches the parabola at exactly two points located symmetrically on opposite sides of the y-axis, as shown in the diagram. Deduce that c>1/2
so in the diagram, the parabola has vertex (0,0) and is positive for all values of x, and (o,c) is above the two points of intersection.
this was 2012 Q16c) HSC question
Click here to see answer by Edwin McCravy(20056)

Question 1133039: hallar la ecuacion de las hiperbolas determinadas por:
1) vertices (+-1,0) asíntotas y=+-5x
2) focos (0,+-6) pasa por P=(-5,9)
3) focos (0,+-1) longitud eje real:1
4) asíntotas y= +- x/2 pasa por el punto de coordenadas (5,2)
Click here to see answer by MathLover1(20850)

Question 1133407: You have a parable with the points -2,0 and 4,0 and a vertex of 0,-3 put into y=a(x-h)^2 +k
Click here to see answer by Alan3354(69443)

Question 1133444:
Click here to see answer by ikleyn(52795)

Question 1133782: trying to find the vertex, focus, latus rectum, directrix, axis of symmetry for the following equation
-2(x+3)=(y-1)^2
Click here to see answer by MathLover1(20850)

Question 1133952: Find the locus of a point P(x,y) which moves so that area triangle APB is 5 u^2 where A(-4,0) and B(2,0)
Click here to see answer by greenestamps(13200)

Question 1133952: Find the locus of a point P(x,y) which moves so that area triangle APB is 5 u^2 where A(-4,0) and B(2,0)
Click here to see answer by ikleyn(52795)

Question 1133953: Find the locus of a point P(x,y) which moves so that area triangle APB is 5 u^2 where A(-4,0) and B(2,0).
Click here to see answer by greenestamps(13200)

Question 1134109: 4x^2+4y+8x=15 I need help writing it in standard form. (X-h)=4p(y-k)
Click here to see answer by JaydenX(2)

Question 1134109: 4x^2+4y+8x=15 I need help writing it in standard form. (X-h)=4p(y-k)
Click here to see answer by josgarithmetic(39618)

Question 1134505: Find an equation of the circle whose diameter has endpoints (-5,-5) and (3,1)

Click here to see answer by mathsolverplus(88)

Question 1134505: Find an equation of the circle whose diameter has endpoints (-5,-5) and (3,1)

Click here to see answer by josmiceli(19441)

Question 1134506: Find an equation of the circle whose diameter has endpoints (-3,2) and (2,2)

Click here to see answer by mathsolverplus(88)

Question 1134506: Find an equation of the circle whose diameter has endpoints (-3,2) and (2,2)

Click here to see answer by ikleyn(52795)

Question 1134394: A point P(2p,p^2) lie on x^2=4ay. The perpendicular, from the focus S of the parabola, on to the tangent cuts the directrix at M. If N is the midpoint of the interval PM, find the equation of the locus of N.
I keep getting long equations that I don't know how to simplify. Right now I have this: 2y+4ay+2a^y=x^2-a-2a^2-a^3
Click here to see answer by t0hierry(194)

Question 1134790: Find an equation in standard form for the ellipse that satisfies the given conditions.
Major axis endpoints (6,6) and (6,-12), minor axis length 4.
Click here to see answer by MathLover1(20850)

Question 1134791: Find an equation in standard form for the hyperbola that satisfies the given conditions.
Center at (0,0) a=4, e=4, horizontal focal axis
Click here to see answer by MathLover1(20850)

Question 1135422: write the equation of the hyperbola in standard form given the corners of refrence rectangle (19,15),(19,-1),(-15,-1),(-15,15) and horizontal transverse axis.
Click here to see answer by greenestamps(13200)

Question 1135868: it is given that sin A = K, where A is an angle measured in radians,
and pi < A < (3pi/2)
If sin B = k, which of the following is the value of B?
A) A - pi
B) pi + A
C) 2pi - A
D) 3pi - A
Click here to see answer by jim_thompson5910(35256)

Question 1136329: Write the standard form of the equation of the parabola with focus at (-2, 5) and directrix at
x = 4.
Click here to see answer by josgarithmetic(39618)

Question 1136333: Use the discriminant to determine whether the equation represents a parabola, hyperbola, or
an ellipse. 4x^2 - 9xy - 5y^2 + 15 = 0
Click here to see answer by MathLover1(20850)

Question 1136330: Find the equation in standard form of the hyperbola that has foci at (8, 1)(-8, 1) and
transverse axis with length 14.
Click here to see answer by MathLover1(20850)

Question 1136328: Find the polar equation of an ellipse with a focus at the pole and major axis endpoints (4, 0)
and (2, 𝞹).
Click here to see answer by MathLover1(20850)

Question 1136327: Find the polar equation of the conic with focus at the pole, having eccentricity 5 and
directrix y = -6.
Click here to see answer by MathLover1(20850)

Question 1136722: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.
Horizontal axis and passes through the point (−2, 5)
Click here to see answer by josgarithmetic(39618)

Question 1136776: Hello! If someone could please help me solve this equation, I would be very grateful.
Find an equation for the ellipse with vertices at (-3, 4) and (15, 4); focus at (13, 4)
Click here to see answer by MathLover1(20850)

Question 1136852: Hi. I am having a very tough time with the conic sections portion of my algebra class. Is there anyway someone can help me solve the equation:
Find the center, transverse axis, vertices, and foci of the hyperbola: y^2/81 - x^2/64 = 1
any help would be sincerely grateful!
Thank you in advance for any help!
Click here to see answer by ikleyn(52795)

Question 1136851: Hi. I am having a very tough time with the conic sections portion of my algebra class. Is there anyway someone can help me solve the equation:
Find an equation for the hyperbola with vertices at (0, -6) and (0, 6); asymptote the line y=3/5x
any help would be sincerely grateful!
Thank you in advance for any help!
Click here to see answer by greenestamps(13200)

Question 1136893: Which is the equation of a parabola with Vertex (0, 0) and directrix x = -2?
Click here to see answer by Alan3354(69443)

Question 1136928: Determine the standard form of the equation of the line that passes through (-7,8)and (0,2)
Click here to see answer by MathLover1(20850)

Question 1137060: Find an equation of the ellipse that has center (1,1) a major axis of length of 10 , and endpoint of minor axis (0,1)
Click here to see answer by ikleyn(52795)

Question 1137062: Find an equation of the ellipse that has center (-5,5), a minor axis of length 4, and a vertex at (4,5).
Click here to see answer by MathLover1(20850)

Question 1137062: Find an equation of the ellipse that has center (-5,5), a minor axis of length 4, and a vertex at (4,5).
Click here to see answer by ikleyn(52795)

Question 1137076: Find an equation of the ellipse that has center (5,-1)
, a major axis of length 4
, and endpoint of minor axis (6,-1)
.
Click here to see answer by ikleyn(52795)

Question 1137157: Find an equation of the ellipse that has center (-2,5)
, a minor axis of length 10
, and a vertex at (9,5)
.
Click here to see answer by MathLover1(20850)

Question 1137157: Find an equation of the ellipse that has center (-2,5)
, a minor axis of length 10
, and a vertex at (9,5)
.
Click here to see answer by ikleyn(52795)

Question 1137164: Find an equation of the ellipse that has center (5,-4)
, a minor axis of length 8
, and a vertex at (0,-4)
.
Click here to see answer by ikleyn(52795)

Question 1137164: Find an equation of the ellipse that has center (5,-4)
, a minor axis of length 8
, and a vertex at (0,-4)
.
Click here to see answer by MathLover1(20850)

Question 1137166: ``Find an equation of the ellipse that has center (5,-4)
, a minor axis of length 8
, and a vertex at (0,-4)
THIS IS THE ANSWER I GOT I WANT TO MAKE SURE IT IS CORRECT
(x-5)^2 / 25 + (y+4)^2 / 16 =1
Click here to see answer by MathLover1(20850)

Question 1137082: Find an equation of the ellipse that has center (-2,5)
, a minor axis of length 10
, and a vertex at (9,5)
.

Click here to see answer by greenestamps(13200)

Question 1137550: A skateboarder decides to jump off a ramp. The path of the jump from the ramp can be approximated by: h=-3t^2+6t+1, where h is the height above the ground in metres, s is the horizontal displacement and t is the time after leaving the ramp in seconds. Show that the maximum height reached by the skateboarder is 4m.
Click here to see answer by Boreal(15235)

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