Analytic Geometry Practice Questions – Mathematics (Page 9)

#12977📜 CE Board November 1992Problem

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

#12978Problem

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\(x=16\)

#12979Problem

What is the length of the latus rectum of \(4x^2+9y^2+8x-32=0\)?

A2.5

B2.7

C2.3

D2.9

#12980📜 EE Board October 1993Problem

\(4x^2-y^2=16\) is the equation of a/an

Aparabola

Bhyperbola

Ccircle

Dellipse

#12981📜 EE Board October 1993Problem

Find the eccentricity of the curve \(9x^2-4y^2-36x+8y=4\)

A1.80

B1.92

C1.86

D1.76

#12982📜 CE Board November 1995Problem

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

#12983📜 EE Board October 1994Problem

The semi-transverse axis of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) is

A2

B3

C4

D5

#12984📜 CE Board May 1996Problem

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\(2x+y=0\)

#12985📜 EE Board April 1994Problem

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\(4x^2-y^2=16\)

#12986Problem

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\(5x^2+4y^2-20x+16y-16=0\)

#12987Problem

Find the distance between \(P_1(6,-2,-3)\) and \(P_2(5,1,-4)\).

A11

B\(\sqrt{11}\)

C12

D\(\sqrt{12}\)

#12988Problem

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)

#12989📜 ME Board April 1997Problem

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

#12990Problem

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\(x^2+y^2+z^2+6x-4y+8z=36\)

#12991📜 EE Board April 1997Problem

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\(r-4 \cos \theta=0\)

#12992📜 ME Board October 1996Problem

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)

#12993Problem

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\(r=9 \sin \theta\)

#12994📜 EE Board October 1997Problem

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)