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
#162
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\(x=16\)
#163
What is the length of the latus rectum of \(4x^2+9y^2+8x-32=0\)?
A2.5
B2.7
C2.3
D2.9
#164📜 EE Board October 1993
\(4x^2-y^2=16\) is the equation of a/an
Aparabola
Bhyperbola
Ccircle
Dellipse
#165📜 EE Board October 1993
Find the eccentricity of the curve \(9x^2-4y^2-36x+8y=4\)
A1.80
B1.92
C1.86
D1.76
#166📜 CE Board November 1995
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
#167📜 EE Board October 1994
The semi-transverse axis of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) is
A2
B3
C4
D5
#168📜 CE Board May 1996
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\(2x+y=0\)
#169📜 EE Board April 1994
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\(4x^2-y^2=16\)
#170
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\(5x^2+4y^2-20x+16y-16=0\)
#171
Find the distance between \(P_1(6,-2,-3)\) and \(P_2(5,1,-4)\).
A11
B\(\sqrt{11}\)
C12
D\(\sqrt{12}\)
#172
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)
#173📜 ME Board April 1997
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
#174
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\(x^2+y^2+z^2+6x-4y+8z=36\)
#175📜 EE Board April 1997
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\(r-4 \cos \theta=0\)
#176📜 ME Board October 1996
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)
#177
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\(r=9 \sin \theta\)
#178📜 EE Board October 1997
Given the polar equation \(r=5 \sin \theta\). Determine the rectangular coordinates (x,y) of a point in the curve when \(\theta\) is \(30^\circ\).
