What is the length of the length of the latus rectum of the curve \(x^2=20y\)?
A\(\sqrt{20}\)
B20
C5
D\(\sqrt{5}\)
Mathematics · Question Bank
Analytic Geometry
189 of 233 questions match · page 7 of 10. Answer in your head first, then check the solution.
Find the location of the focus of the parabola \(y^2+4x-4y-8=0\).
A(2.5,-2)
B(3,1)
C(2,2)
D(-2.5,-2)
Find the equation of the axis of symmetry of the function \(y=2x^2-7x+5\)
A\(7x+4=0\)
B\(4x+7=0\)
C\(4x-7=0\)
D\(x-2=0\)
A parabola has its focus at \((7,-4)\) and directrix \(y=2\). Find its equation.
A\(x^2+12y-14x+61=0\)
B\(x^2-14y+12x+61=0\)
C\(x^2-12x+14y+61=0\)
DNone of the above
A parabola has its axis parallel to the x-axis, vertex at \((-1,7)\) and one end of the latus rectum at \((-15/4,3/2)\). Find its equation.
A\(y^2-11y+11x-60=0\)
B\(y^2-11y+14x-60=0\)
C\(y^2-14y+11x+60=0\)
DNone of the above
Compute the focal length and the length of the latus rectum of the parabola \(y^2+8x-6y+25=0\)
A2, 8
B4, 16
C16, 64
D1, 4
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\(B^2-4AC=1\)
What is the area enclosed by the curve \(9x^2+25y^2-225=0\)?
A47.1
B50.2
C63.8
D72.3
Point \(P(x,y)\) moves with a distance from point \((0,1)\) one-half of its distance from line \(y=4\). The equation of its locus is
A\(2x^2-4y^2=5\)
B\(4x^2+3y^2=12\)
C\(2x^2+5y^2=3\)
D\(x^2+2y^2=4\)
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 equation \(25x^2+16y^2-150x+128y+81=0\) has its center at
A(3,-4)
B(3,4)
C(4,-3)
D(3,5)
Find the major axis of the ellipse \(x^2+4y^2-2x-8y+1=0\)
A2
B10
C4
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
An ellipse with an eccentricity of \(0.65\) and has one of its foci \(2\) units from the center. The length of the latus rectum is nearest to
A3.5 units
B3.8 units
C4.2 units
D3.2 units
An earth satellite has an apogee of \(40{,}000\) km and a perigee of \(6{,}600\) km. Assuming the radius of the earth as \(6{,}400\) km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci?
A0.46
B0.49
C0.52
D0.56
The major axis of the elliptical path in which the earth moves around the sun is approximately \(186{,}000{,}000\) miles and the eccentricity of the ellipse is \(1/60\). Determine the apogee of the earth.
A93,000,000 miles
B91,450,000 miles
C94,335,100 miles
D94,550,000 miles
The earth's orbit is an ellipse with the sun at one of the foci. If the farthest distance of the sun from the earth is \(105.50\) million km and the nearest distance of the sun from the earth is \(78.25\) million km, find the eccentricity of the ellipse.
A0.15
B0.25
C0.35
D0.45
An ellipse with center at the origin has a length of major axis \(20\) units. If the distance from center of ellipse to its focus is \(5\), what is the equation of its directrix?
A\(x=18\)
B\(x=20\)
C\(x=15\)
D\(x=16\)
What is the length of the latus rectum of \(4x^2+9y^2+8x-32=0\)?
A2.5
B2.7
C2.3
D2.9