Find the standard equation of the circle with the center at (1, 3) and tangent to the line \(5x - 12y - 8 = 0\).
A\((x-1)^2 + (y-3)^2 = 8\)
B\((x-1)^2 + (y-3)^2 = 12\)
C\((x-1)^2 + (y-3)^2 = 9\)
D\((x-1)^2 + (y-3)^2 = 23\)
Mathematics · Question Bank
Analytic Geometry
233 questions · page 10 of 12. Answer in your head first, then check the solution.
If the vertex of \(y = 2x^2 + 4x + 5\) is shifted 3 units to the left and 2 units downward, what will be the new location of the vertex?
A(−2, 1)
B(−5, −1)
C(−3, 1)
D(−4, 1)
The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between two towers is 150 m, the points of the cable on the towers are 22 m above the roadway, and the lowest point on the cable is 7 m above the roadway. Find the vertical distance to the cable from a point in the roadway 15 m from the foot of a tower.
A16.6 m
B9.6 m
C12.8 m
D18.8 m
In the polar coordinate system, the distance from a point to the pole is known as the
Apolar angle
Bx-coordinate
Cradius vector
Dy-coordinate
If the equation is unchanged by the substitution of −x for x, its curve is symmetric with respect to the
Ay-axis
Bx-axis
Corigin
Dline 45 degrees with the axis
What conic section is represented by \(2x^2 + y^2 - 8x + 4y = 16\)?
Aparabola
Bellipse
Chyperbola
Dcircle
What is the length of the line with a slope of 4/3 from a point (6, 4) to the y-axis?
A10
B25
C50
D75
The inclination of the line determined by the points (4, 0) and \((5, \sqrt{3})\) is
A30 degrees
B45 degrees
C60 degrees
D90 degrees
How many petals are there in the rose curve \(r = 3\cos 5\theta\)?
A5
B10
C15
D6
A conic section whose eccentricity is equal to one (1) is known as
Aa parabola
Ban ellipse
Ca circle
Da hyperbola
In a conic section, if the eccentricity is greater than one (1), the locus is
Aa parabola
Ban ellipse
Ca circle
Da hyperbola
How far is the directrix of the parabola \((x - 4)^2 = -8(y - 2)\) from the x-axis?
A2
B3
C4
D1
The equations of two lines are \(3y - 2x = 6\) and \(3x + ky = -7\). For what value of k will the two lines be parallel?
A−9/2
B9/2
C−7/3
D7/3
The vertex of the parabola \(y = (x - 1)^2 + 2\) is ______.
A(−1, 2)
B(1, 2)
C(1, −2)
D(−1, −2)
In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a:
Alatus rectum
Bminor axis
Cfocal width
Dconjugate axis
What kind of graph has \(r = 2\sec\theta\)?
Astraight line
Bparabola
Cellipse
Dhyperbola
The axis of the hyperbola through its foci is known as the
Aconjugate axis
Bmajor axis
Ctransverse axis
Dminor axis
Classify the graph of the equation \(x^2 + xy + y^2 - 6 = 0\).
Acircle
Bparabola
Cellipse
Dhyperbola
If the parabola \(y = x^2 + C\) is tangent to the line \(y = 4x + 3\), find the value of C.
A4
B7
C6
D5
A parabola having its axis along the x-axis passes through (−3, 6). Compute the length of the latus rectum if the vertex is at the origin.
A12
B8
C6
D10