What are the coordinates of the center of the curve \(x^2+y^2-2x-4y-31=0\)?
A(-1,-1)
B(-2,-2)
C(1,2)
D(2,1)
Mathematics · Question Bank
Analytic Geometry
128 of 233 questions match · page 4 of 7. Answer in your head first, then check the solution.
A circle whose equation is \(x^2+y^2+4x+6y-23=0\) has its center at
A(2,3)
B(3,2)
C(-3,2)
D(-2,-3)
What is the radius of a circle with the ff. equation: \(x^2-6x+y^2-4y-12=0\)
A3.46
B7
C5
D6
The diameter of a circle described by \(9x^2+9y^2=16\) is
A\(4/3\)
B\(16/9\)
C\(8/3\)
D4
The equation \(x^2+y^2-4x+2y-20=0\) describes:
AA circle of radius 5 centered at the origin.
BAn ellipse centered at (2,-1).
CA sphere centered at the origin.
DA circle of radius 5 centered at (2,-1).
Find the area (in square units) of the circle whose equation is \(x^2+y^2=6x-8y\)
A\(20 \pi\)
B\(22 \pi\)
C\(25 \pi\)
D\(27 \pi\)
\(3x^2+2x-5y+7=0\). Determine the curve.
AParabola
BEllipse
CCircle
DHyperbola
The focus of the parabola \(y^2=16x\) is at
A(4,0)
B(0,4)
C(3,0)
D(0,3)
Where is the vertex of the parabola \(x^2=4(y-2)\)?
A(2,0)
B(0,2)
C(3,0)
D(0,3)
Find the equation of the directrix of the parabola \(y^2=16x\).
A\(x=2\)
B\(x=-2\)
C\(x=4\)
D\(x=-4\)
In the equation \(y=-x^2+x+1\) where is the curve facing?
AUpward
BFacing left
CFacing right
DDownward
What is the length of the length of the latus rectum of the curve \(x^2=20y\)?
A\(\sqrt{20}\)
B20
C5
D\(\sqrt{5}\)
Given a parabola \((y-2)^2=-8(x-1)\). What is the equation of its directrix?
A\(x=-3\)
B\(x=3\)
C\(y=-3\)
D\(y=3\)
The general equation of a conic section is given by the following equation: \(Ax^2+Bxy+Cy^2+Dx+Ey+F=0\). A curve maybe identified as an ellipse by which of the following conditions?
A\(B^2-4AC<0\)
B\(B^2-4AC=0\)
C\(B^2-4AC>0\)
D\(B^2-4AC=1\)
The lengths of the major and minor axes of an ellipse are \(10\) m and \(8\) m, respectively. Find the distance between the foci.
A3
B4
C5
D6
The length of the latus rectum for the ellipse \(\frac{x^2}{64}+\frac{y^2}{16}=1\) is equal to
A2
B3
C4
D5
\(4x^2-y^2=16\) is the equation of a/an
Aparabola
Bhyperbola
Ccircle
Dellipse
The semi-transverse axis of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) is
A2
B3
C4
D5
Find the distance between \(P_1(6,-2,-3)\) and \(P_2(5,1,-4)\).
A11
B\(\sqrt{11}\)
C12
D\(\sqrt{12}\)
What is the radius of the sphere center at the origin that passes the point 8,1,6?
A10
B9
C\(\sqrt{101}\)
D10.5