What is the curve represented by the equation r = aθ ?

Is the locus of a point that moves in a plane so that the difference of the distances from two fixed points of the locus is constant.

The semi-conjugate axis of the hyperbola (x^2/9) – (y^2/4) = 1

The length of the latus rectum of the parabola y = 4px^2 id

The tangent function is negative in what quadrants?

The Cartesian or rectangular coordinates system was first introduces by

Also known as the x-coordinate

The x-coordinate of a point is positive in what quadrants?

The y-coordinate of a point is positive in what quadrants?

State the quadrants in which the coordinates (15, -2) lies.

The rectangular coordinates system used to represent a complex number.

A Cartesian coordinates system in which the axes are not perpendicular.

The angle of rotation about the origin of the positive x-axis into the point with rectangular coordinates (a, b), representing the complex number a + bi is called of the complex number.

The rectangular coordinates system in space is divided into eight compartments called

The angle of inclination of a straight line is the angle it makes with the

The points where the curve crossed the coordinates axes are called the with the axes.

A line which is perpendicular to the x-axis has slope equal to

A horizontal line has a slope of

A line parallel to the y-axis at a directed distance x_1 has the equation

Let m_1 and m_2 be the respective slopes of two perpendicular lines. Then

If all the y-terms have even exponents, the curve is symmetric with respect to the

If the equation is unchanged by the substitution of –x for x and –y for y simultaneously, its curve is symmetric with respect to the

If all of the terms of an equation have an exponenets of if all of the terms have odd exponents, the curve is symmetric with respect to the

If two linear equations, the x-coefficient of the first is equal to the y-coefficient of the send and the y-coefficient of the first is numerically equal but of opposite sign to the x-coefficient of the second, or vice-versa, the lines represented are

A cubic equation has either three real roots or one real root and two conjugate imaginary roots. The real roots are the points of intersection with

If two equations have the same line as their graph, the equations are said to be

The points (a, 1), (b, 2), (c, 3) are collinear. Which of the following is TRUE?

In a linear equation Ax + By + C = 0, if B = 0, then the equation has the form of x = -C/A. This line is

The straight lines 4x – y + 3 = 0 and 8x – 2y + 6 = 0 are

Which of the following is the intercept form of an equation for straight lines?

A straight line where the curve approaches more and more closely but never touches it except at a limiting point of infinity.

Who coined the word “asymptote”?

The path of a point which moves according to a given law or equation.

The curve traced by a point moving in a plane is shown as the of the point.

A conic section is curve which is the intersection of

When the ellipse approaches a circle as a limiting shape, its eccentricity approaches

The set of points in a plane, the sum of whose distances from a fixed points is constant, is

If a right circular cone is cut by a plane parallel to its bas, it would reveal a/an

A to a circle is a line that has exactly one point in common with the circle.

A conic section whose eccentricity is always less than 1.

A locus of appoint which moves so that the sum of the distances from two fixed points (foci) is constant and is equal to the length of the major axis.

If the distance from the center to the focus of an ellipse is c, from the center to the vertex is a and from the center to the directrix is D, its eccentricity, is

A locus of a point which move so that it is always equidistant from a fixed point (focus) and from a fixed straight line (directrix)

The angle between the tangents at the end points of the latus rectum of a parabola is

The tangents to the parabola at the end points of its latus rectum intersect

In general equation of a conic section Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, if A and C have different signs, then the curve is a/an

If the discriminant of a quadratic equation is greater than zero, the graph is a/an

The graph is a/an

A chord passing through the focus of a parabola and perpendicular to the axis of symmetry

The graph of the equation r = a cos 2θ is a

The locus of a point which rolls on a straight line (x-axis)

The equation r = a (1+cosθ) is a polar equation of

The equation r^2 = a^2 cosθ is a

The equation r = a cosθ is a

The equation r – aθ = 0 is a

The equation r = a cosθ + b is a

The equation r = a(secθ – tanθ) is a

The equation r = a(4cosθ – secθ) is a

The equation (x^2 + 2ay – a^2) = y^2 (a^2 – x^2) is a

The equation x^2 + y^2 = a^2

The equation ax^2 = y^2 (2a – y) is the equation of

The equation (x^2 _ y^2) = a x^2 y^2 is an equation of

The equation y^2 = (x^2 + 1^2)^2 (2 – x^2)^3 is an equation of

A curve or surface that is tangential to each of the family of curves or surfaces.

A curve that describes the locus of the centers of curvatures of another curve to which its tangents are normal.

is formed by intersection of rays from the point reflected or refracted from a curve surface.

When f”(x) is negative the curve of y = f(x) is concave.

If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is

A function F(x) is called of f(x) if F’(x) = f(x).

Points of derivatives which do not exists (and so equals zero) are called .

At the point of inflection where x = a,

At the minimum point, the slope of the tangent line is

What is the point where the second derivative is zero?

The point on the curve where the second derivative of a function is equal to zero is called

The point of the curve where the first derivative of a function is zero and the second derivative is positive is called

Evaluate the integral of tanh u du.

The derivative of a^u with respect to x is

If y = tanhx, find dy/dx.

The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton and Leibniz

The of a relation is the set of second elements of the pair in the relation

A relation in which there is exactly one range element associated with each domain element

The of a relation is the set of first elements of pairs in the relation.

Any set of ordered pair is called a

Any pair of elements (x, y) having a first element x and a second element y is called

The operation of finding the derivative of a function

The derivative of a function is identical to the of the graph of the function

The derivative of the function is the rate of change of the slope is also known as the composite function rule of the graph

A point on the graph where the tangent line is either horizontal or vertical is known as

The critical points of a graph occur when the derivative of a function is

At point of inflection,

At a point where y’ = 0, if y changes from positive to negative as x increases

The point where the second derivative of a function is zero

The point where the first derivative of a function is zero and the second derivative is positive

A point at which the curve changes from concave upward to concave downward and vice versa is known as

At a point where y’ = 0, if y changes from positive to negative as x increases

At maximum point,

The L’Hospital rule was formulated by

A collective term for maxima or minima, whether absolute of relative is called

Which of the following is not determinate form?

Which of the following is determinate?

The derivative of csc θ is

Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of

The quantity 2/(e^x – e^-x) is equal to

What is 1 – tan h^2 x equal to?