Analytic Geometry Practice Questions – Mathematics (Page 7)

#12937📜 ECE Board April 1999Problem

Two vertices of a triangle are \((2,4)\) and \((-2,3)\) and the area is \(2\) square units, the locus of the third vertex is

A\(4x-y=14\)

B\(4x+4y=14\)

C\(x+4y=12\)

D\(x-4y=-14\)

#12938📜 ECE Board April 1998Problem

Find the area of the triangle which the line \(2x-3y+6=0\) forms with the coordinate axis.

A3

B4

C5

D2

#12939📜 ECE Board November 1998Problem

A line passes through point \((2,2)\). Find the equation of the line if the length of the line segment intercepted by the coordinates axes is the square root of \(5\).

A\(2x+y-2=0\)

B\(2x-y-2=0\)

C\(2x-y+2=0\)

D\(2x+y+2=0\)

#12940📜 CE Board May 1995Problem

What is the radius of the circle \(x^2+y^2-6y=0\)?

A2

B3

C4

D5

#12941📜 CE Board November 1995Problem

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)

#12942Problem

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)

#12943📜 ME Board April 1998Problem

What is the radius of a circle with the ff. equation: \(x^2-6x+y^2-4y-12=0\)

A3.46

B7

C5

D6

#12944📜 ECE Board April 1998Problem

The diameter of a circle described by \(9x^2+9y^2=16\) is

A\(4/3\)

B\(16/9\)

C\(8/3\)

D4

#12945📜 CE Board May 1996Problem

How far from the y-axis is the center of the curve \(2x^2+2y^2+10x-6y-55=0\)?

A-2.5

B-3.0

C-2.75

D-3.25

#12946Problem

What is the distance between the centers of the circles \(x^2+y^2+2x+4y-3=0\) and \(x^2+y^2-8x-6y+7=0\)?

A7.07

B7.77

C8.07

D7.87

#12947📜 CE Board November 1993Problem

The shortest distance from A (3,8) to the circle \(x^2+y^2+4x-6y=12\) is equal to

A2.1

B2.3

C2.5

D2.7

#12948📜 ME Board October 1996Problem

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).

#12949📜 EE Board April 1997Problem

The center of a circle is at \((1,1)\) and one point on its circumference is \((-1,-3)\). Find the other end of the diameter through \((-1,-3)\).

A(2,4)

B(3,5)

C(3,6)

D(1,3)

#12950Problem

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\(27 \pi\)

#12951Problem

Determine the equation of the circle whose radius is 5, center on the line \(x=2\) and tangent to the line \(3x-4y+11=0\).

A\((x-2)^2+(y-2)^2=5\)

B\((x-2)^2+(y+2)^2=25\)

C\((x-2)^2+(y+2)^2=5\)

D\((x-2)^2+(y-2)^2=25\)

#12952Problem

Find the equation of the circle with the center at \((-4,-5)\) and tangent to the line \(2x+7y-10=0\)

A\(x^2+y^2+8x-10y-12=0\)

B\(x^2+y^2+8x-10y+12=0\)

C\(x^2+y^2+8x+10y-12=0\)

D\(x^2+y^2-8x+10y+12=0\)

#12953📜 ECE Board April 1998Problem

Find the value of k for which the equation \(x^2+y^2+4x-2y-k=0\) represents a point circle.

A5

B6

C-6

D-5

#12954📜 ECE Board April 1999Problem

\(3x^2+2x-5y+7=0\). Determine the curve.

AParabola

BEllipse

CCircle

DHyperbola

#12955📜 CE Board May 1993, CE Board November 1993, ECE Board April 1994Problem

The focus of the parabola \(y^2=16x\) is at

A(4,0)

B(0,4)

C(3,0)

D(0,3)

#12956📜 CE Board November 1994Problem

Where is the vertex of the parabola \(x^2=4(y-2)\)?

A(2,0)

B(0,2)

C(3,0)

D(0,3)