Analytic Geom Flashcards by JM Park

In general, quadratic equation, if the discriminant is zero, the curve is a figure that represent a/an

Parabola

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Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. Such equations may nonetheless determine y as a function of x or vice versa, such function is called

Implicit function

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In polar coordinates system, the length of the ray segment from a fixed origin is known as ____.

Radius vector

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Given the equation 3x2 + 2x – 5y + 7 = 0. determine the curve.

Parabola

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If eccentricity is less than one, then the curve is

Ellipse

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Of what quadrant is A, if sec A is positive and csc A is negative?

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If the general equation of the conic is Ax2 + 2Bxy + Cy2 + Ey + F = 0 and B2 – 4AC > 0, then the conic is a/an

Hyperbola

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What type of conic has equation of Ax2 + Cy2 + Dx + Ey + F = 0?

Ellipse

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The graph of r = a + bcosθ is a

Limacon

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In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is called

Latus rectum

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

X-axis

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It can be defined as the set of all points in the plane the sum of whose distances from two fixed points is constant

Ellipse

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

Y-axis

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What type of curve is generated by a point which moves in uniform circular motion about an axis, while travelling with a constant speed parallel to the axis?

Helix

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It represents the distance of a point from the y-axis

Abscissa

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A line passing through the focus and perpendicular to the directrix of a parabola is called

Axis of parabola

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Locus of points on a side which rolls along a fixed line

Cycloid

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If the product of the slopes of any two straight lines is negative 1, one of these is said to be ____ to the other.

Perpendicular

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

Spiral of Archimedes

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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

Hyperbola

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The length of the latus rectum of the parabola 𝑦 = 4𝑝𝑥2 is

1/4p

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The cartesian or rectangular coordinates system was first introduced by

Descartes

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Also known as the x-coordinate

Abscissa

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

I and IV

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

I and II

The rectangular coordinate system used to represent a complex number

Argand Diagram

A cartesian coordinates system in which the axes are not perpendicular

oblique coordinates system

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

Octants

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

Positive x-axis

The points where the curve crossed the coordinates axes are called as the ___ with the axes

Intersections

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

Infinity

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

x-axis

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

origin

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

origin

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 line represented are

perpendicular to each other

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

dependent

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

parallel to the y-axis

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

Asymptote

Who coined the word “asymptote”?

Thomas Hobbes

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

Locus

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

Locus

A conic section is curve which is the intersection of

a cone and a plane

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 form a fixed point is constant, is

circle

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

circle

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

tangent

A conic section whose eccentricity is always less than 1

ellipse

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

ellipse

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

c/a

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

parabola

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

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

at the directrix

In general equation of a conic section Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, if A and C have different signs, then the curve is a/an

hyperbola

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

hyperbola

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

latus rectum

The latus rectum of the parabola x2 = 4ay is

If a and b are lengths of semi-major and semi-minor axis of an ellipse respectively, then what is the length of its latus rectum?

2b^2/2

The eccentricity of a regular hyperbola is

sqrt. of 2

The axis of the parabola that passes through the foci, vertices and center is called

transverse axis

The locus of a moving point in a plane so that the difference of its distance from two fixed points (foci) is constant

hyperbola

What is the term given to a circle with radius equal to half the transverse axis of the hyperbola or major axis of an ellipse and its center is the center of conics?

auxiliary circle

Which is NOT a central conic?

parabola

Confocal conics are conics

having the same foci

A line segment joining two of its points and passing through a focus of a conic

focal chord

Given the polar equation r = 3 / (1 + 3 cos θ). This is a graph of a/an

hyperbola

The equation r = 4 cos θ is a/an

circle

In polar coordinate system, the distance of any point P from the origin is called

radius vector

The plane curve traced out by a fixed point on the circle as the circle rolls along a line.

cycloid

A plane curve traced by a fixed point on a circle as it rolls along outside of a fixed circle.

epicycloid

A plane curve traced by a fixed point on a circle as it rolls along inside of a fixed circle.

hypocycloid

The equation x3 + y3 – 3ay = 0 represents a

folium of Descartes

Continuous curve traced by a point moving around fixed point in same plane are steadily increasing or decreasing distance

spiral

Locus of the ultimate intersections or curves in a system of curves.

envelope

Curve formed by uniform chain hanging freely from two points.

catenary

The locus of a point such that its radius vector is proportional to its vector angle.

Spiral of Archimedes

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

rosette

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

trochoid

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

cardioids

The equation r^2 = a^2 cos θ is a

lemniscate

The equation r = a cos θ is a

rosette

The equation r – aθ =0 is a

spiral

The equation r = a cos θ + b is a

limacon

The equation r = a (secθ – tan θ) is a

strophoid

The equation r = a (4cosθ – secθ) is a

trisectrix

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

cocked hat

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

lames quartic

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

the top

The equation (x^2 + y^2)^2 = ax^2 y is an equation of

bifolium

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

fish mouth

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

envelope

A curve that describes the locus of the centers of curvatures of another curve to which its tangent is normal

evolute

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

caustic