\(4x^2-y^2=16\) is the equation of a/an
Aparabola
Bhyperbola
Ccircle
Dellipse
Mathematics · Question Bank
Analytic Geometry
189 of 233 questions match · page 8 of 10. Answer in your head first, then check the solution.
Find the eccentricity of the curve \(9x^2-4y^2-36x+8y=4\)
A1.80
B1.92
C1.86
D1.76
How far from the x-axis is the focus F of the hyperbola \(x^2-2y^2+4x+4y+4=0\)?
A4.5
B3.4
C2.7
D2.1
The semi-transverse axis of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) is
A2
B3
C4
D5
What is the equation of the asymptote of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\)?
A\(2x-3y=0\)
B\(3x-2y=0\)
C\(2x-y=0\)
D\(2x+y=0\)
Find the equation of the hyperbola whose asymptotes are \(y=\pm2x\) and which passes through \((5/2,3)\).
A\(4x^2+y^2+16=0\)
B\(4x^2+y^2-16=0\)
C\(x^2-4y^2-16=0\)
D\(4x^2-y^2=16\)
Find the equation of the hyperbola with vertices at \((-4,2)\) and \((0,2)\) and foci at \((-5,2)\) and \((1,2)\).
A\(5x^2-4y^2+20x+16y-16=0\)
B\(5x^2-4y^2+20x-16y-16=0\)
C\(5x^2-4y^2-20x+16y+16=0\)
D\(5x^2+4y^2-20x+16y-16=0\)
Find the distance between \(P_1(6,-2,-3)\) and \(P_2(5,1,-4)\).
A11
B\(\sqrt{11}\)
C12
D\(\sqrt{12}\)
The point of intersection of the planes \(x+5y-2z=9\), \(3x-2y+z=3\) and \(x+y+z=2\) is at
A(2,1,-1)
B(2,0,-1)
C(-1,1,-1)
D(-1,2,1)
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
The equation of a sphere with center at \((-3,2,4)\) and of radius \(6\) units is
A\(x^2+y^2+z^2+6x-4y-8z=36\)
B\(x^2+y^2+z^2+6x-4y-8z=7\)
C\(x^2+y^2+z^2+6x-4y+8z=6\)
D\(x^2+y^2+z^2+6x-4y+8z=36\)
Find the polar equation of the circle, if its center is at \((4,0)\) and the radius \(4\).
A\(r-8 \cos \theta=0\)
B\(r-6 \cos \theta=0\)
C\(r-12 \cos \theta=0\)
D\(r-4 \cos \theta=0\)
What are the x and y coordinates of the focus of the conic section described by the following equation? (Angle \(\theta\) corresponds to a right triangle with adjacent side x, opposite side y and the hypotenuse r.) \(r \sin^2 \theta=\cos \theta\)
A(1/4, 0)
B(0, \(\pi/2\))
C(0, 0)
D(-1/2, 0)
Find the polar equation of the circle of radius \(3\) units and center at \((3,0)\).
A\(r=3 \cos \theta\)
B\(r=3 \sin \theta\)
C\(r=6 \cos \theta\)
D\(r=9 \sin \theta\)
Given the polar equation \(r=5 \sin \theta\). Determine the rectangular coordinates (x,y) of a point in the curve when \(\theta\) is \(30^\circ\).
A(2.17, 1.25)
B(3.08, 1.5)
C(2.51, 4.12)
D(6,3)
Find the area of the triangle which the line \(2x - 3y + 6 = 0\) forms with the coordinate axes.
A3
B4
C5
D2
Find the standard equation of the circle with the center at (1, 3) and tangent to the line \(5x - 12y - 8 = 0\).
A\((x-1)^2 + (y-3)^2 = 8\)
B\((x-1)^2 + (y-3)^2 = 12\)
C\((x-1)^2 + (y-3)^2 = 9\)
D\((x-1)^2 + (y-3)^2 = 23\)
If the vertex of \(y = 2x^2 + 4x + 5\) is shifted 3 units to the left and 2 units downward, what will be the new location of the vertex?
A(−2, 1)
B(−5, −1)
C(−3, 1)
D(−4, 1)
The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between two towers is 150 m, the points of the cable on the towers are 22 m above the roadway, and the lowest point on the cable is 7 m above the roadway. Find the vertical distance to the cable from a point in the roadway 15 m from the foot of a tower.
A16.6 m
B9.6 m
C12.8 m
D18.8 m
What is the length of the line with a slope of 4/3 from a point (6, 4) to the y-axis?
A10
B25
C50
D75