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\(x-4y=-14\)
Mathematics · Question Bank
Analytic Geometry
178 questions · page 7 of 9. Answer in your head first, then check the solution.
Find the area of the triangle which the line \(2x-3y+6=0\) forms with the coordinate axis.
A3
B4
C5
D2
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\(2x+y+2=0\)
What is the radius of the circle \(x^2+y^2-6y=0\)?
A2
B3
C4
D5
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)
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)
What is the radius of a circle with the ff. equation: \(x^2-6x+y^2-4y-12=0\)
A3.46
B7
C5
D6
The diameter of a circle described by \(9x^2+9y^2=16\) is
A\(4/3\)
B\(16/9\)
C\(8/3\)
D4
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
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
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
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).
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)
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\(27 \pi\)
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\((x-2)^2+(y-2)^2=25\)
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\(x^2+y^2-8x+10y+12=0\)
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
\(3x^2+2x-5y+7=0\). Determine the curve.
AParabola
BEllipse
CCircle
DHyperbola
The focus of the parabola \(y^2=16x\) is at
A(4,0)
B(0,4)
C(3,0)
D(0,3)
Where is the vertex of the parabola \(x^2=4(y-2)\)?
A(2,0)
B(0,2)
C(3,0)
D(0,3)