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AGC
| Question | Answer |
|---|---|
| The Cartesian coordinate system is named in honor of the French mathematician | Reneβ Descartes (1596-1650) |
| Cartesian coordinate system is also known as ______. | rectangular coordinate system |
| This system is represented by a plane of two perpendicular real number lines intersecting at the origin O (0, 0). | Cartesian coordinate system |
| The horizontal line is called the ___ while the vertical line is referred to as the ___. | x-axis and y-axis respectively |
| Points that fall on the coordinate axes belong to what quadrant? | They do not belong to any quadrant. |
| Each point P in an xy-plane represents an _____ (π, π). | ordered pair |
| The π here is the x-coordinate (or the _____) of P and b, the y-coordinate (or the ____). | abscissa and ordinate respectively |
| a line in which one direction is chosen as positive and the opposite direction as negative. | Directed Line |
| consisting of any two points and the part between them. | Directed Line Segment |
| the distance between two points either positive or negative depending upon the direction of the line. | Directed Distance |
| The distance of a point from the Y-axis is called _____. | abscissa |
| The distance of a point from the x-axis is called _____. | ordinate |
| The angle of inclination π of a line is the smallest nonnegative formed by the ___ | positive x-axis and the line |
| The _____ is a measure of its steepness. | slope of a line |
| We can find the Area of a Polygon by using their _____ | coordinates |
| The angle of inclination π of a line is the _____________. | smallest nonnegative formed by the positive x-axis and the line. |
| The slope of the line defined by π1π2 is the ______________. | tangent of the angle the line makes with the x-axis. |
| ____________, if the line is leaning to the right. | Slope is positive (+), |
| __________________, if the line is leaning to the left. | Slope is negative (-) |
| ___________, if the line is horizontal. | Slope is zero (0) |
| ___________, if the line is vertical. | Slope is undefined ( ) |
| In the angle of inclination of a nonvertical line. If the terminal side of the angle lies on the first quadrant we use the formula: | tan^-1 m = angle |
| In the angle of inclination of a nonvertical line. If the terminal side of the angle lies on the second quadrant we use the formula: | tan^-1 m = angle + 180 |
| In the case that the denominator in the right-hand is zero in angle between two lines, ie. m1m2 = -1, then the angle between these two lines must be __. | 90 degrees |
| The general form of the equation of a line is given by: | Ax + By + C = 0 |
| The standard form of the equation of a line is | Ax + By = C |
| The point-slope form of a line is | y - y1 = m(x - x1) |
| T or F. Multiplying nonzero real number to the equation of a line will not affect the solutions to the equation. Hence, they are equivalent on xy-plane. That is, they have different form but represents the same line. | T |
| The distances from the origin to the points where a line cuts through the axes are called ___________. | intercepts |
| The distance from the origin to the point where the line crosses y-axis is called ___________ and __________ for the distance between the origin to point where to line crosses the x-axis. | y-intercept; x-intercept |
| The slope-intercept form of the equation of a line is given by: | y = mx + b |
| The standard form of the equation of a line in intercepts form is: | x/a + y/b = 1 |
| The equation of the line determined by its perpendicular from the origin is | x cos πΌ + y sin πΌ - p = 0 |
| x cos πΌ + y sin πΌ - p = 0: π is the length of the ____________. | perpendicular |
| x cos πΌ + y sin πΌ - p = 0: πΌ is the __________ makes with the x-axis. | angle the perpendicular |
| x cos πΌ + y sin πΌ - p = 0 is called the ____ form of the equation of the line. | Normal Form |
| In transforming general equation of line Ax + By + C = 0 to its normal form, we can directly divide each term by | sqrt of π΄^2 + π΅^2 |
| Any horizontal lines has standard equation of __________. | y = b where y = 0 refers to the y-axis |
| Any vertical lines has standard equation _______. | x = a where y = 0 refers to the x-axis |
| Two lines πΏ1 and πΏ2 are said to be _______ if and only if they do not have the same point. That is, they do not intersect anywhere in the plane. | parallel |
| m1 = m2 | parallel and collinear |
| Since parallel lines do not intersect anywhere in the ππ- plane, then ____ angle between these lines is formed. | no angle |
| Two lines πΏ1 and πΏ2 are said to be _________ if and only if they have the same ordered pairs. | collinear |
| Since colinear lines have the same set of points, then their graph coincides. Thus, they form a __ angle. | 0Β° |
| Two lines πΏ1 and πΏ2 are said to be _______ if they intersect at a right angle. | perpendicular |
| To verify that the given lines are perpendicular, it suffices to show the relation | π1 = β 1/ π2 |
| From the definition, perpendicular lines form a __ angle. | ππΒ° |
| A ________ is a locus (graph) of a point which moves so that the ratio of its distance from a fixed point (called the focus) to a fixed line (called the directrix) remains constant, the point being always in the plane of the focus and directrix | conic |
| The constant ratio is called the __________ of the conic | eccentricity(π) |
| the three conic sections are defined according to eccentricities as follows If π<1, the conic is an ______ If π=1, the conic is a _______ If π>1 the conic is a _____ | If π<1, the conic is an ellipse If π=1, the conic is a parabola If π>1 the conic is a hyperbola |
| The perpendicular line to the directrix to the focus of a conic is called its ___ | principal axis |
| The points that cut through the principal axis are called the _______ of a conic | vertices of a conic |
| The point that bisects segment whose endpoints are the vertices is called the ____ of a conic. | center |
| The chord through the focus perpendicular to the principal axis is called the _________. | Latus Rectum |
| A _______ is the graph of a point which moves in a plane so as to be of constant distance from a fixed point The fixed point is called center and radius refers to the constant distance | Circle |
| A circle is the graph of a point which moves in a plane so as to be of constant distance from a fixed point. The fixed point is called ________ refers to the constant distance | center and radius |
| Note that a diameter is a _____ that passes through the center of a circle | chord |
| A round plane figure whose boundary consists of points equidistant from a fixed point. | Circle |
| The _______ of the circle is the fixed point from which all points on the boundary of the circle are equidistant. | center |
| The ___ of the circle is half the diameter of the circle. | radius |
| The distance across the circle going through the center. | Diameter |
| The distance once around the circle. | Circumference |
| A part of the circumference. | Arc |
| A ____ is greater than half the circumference. | Major arc |
| A____ is less than half the circumference. | Minor arc |
| A line segment going from one point of the circumference to another but does not go through the center. | Chord |
| A line that goes through the circle at two points. | Secant |
| A straight line that touches the circle at a single point only. | Tangent |
| A section of the circle created by two radii. | sector |
| A section of the circle created by a chord. | Segment |
| Not all equations of the form π₯^2+π¦^2+π·π₯+πΈπ¦+πΉ=0 represents a circle. It could be a ________ | point or a nonempty set |
| It represents a circle if there are __________ solutions | infinitely many |
| A tangent line is a line that intersects a circle at one point and the point at which the circle and the line intersect is the ________. | point of tangency |
| A parabola is a type of conic section whose eccentricity is ___. | π = 1 |
| A _____ as the locus of a point that moves in a plane so that its distance from a fixed point (Focus) is equal to its distance from a fixed line (Directrix). | Parabola |
| The direction of the focus in reference to the vertex is the same as the ____ of the parabola. | opening |
| What connect section is this: D=0; AC =0 | parabola |
| What connect section is this: D>0; AC<0 | hyperbola |
| What connect section is this: D<0; AC = C | Circle |
| What connect section is this: D<; AC > 0 | ellipse |
| What connect section is this: e =1 | parabola |
| What connect section is this: e <1 | ellipse |
| What connect section is this: e >1 | hyperbola |
| formula in solving discriminant | D=B^2 - 4AC |
| The minimum length of a horizontal line segment joining point (π₯, π¦) and π¦ β ππ₯ππ is determined by the abscissa (x coordinate) of the point on the right minus the abscissa (x coordinate) of the point on the left | Horizontal distance of a point |
| A method for finding the area of any polygon when the coordinates of its vertices are known. | Area of a Polygon (Coordinate Geometry) |
| A line segment may be divided by a point called a ____________ either internally or externally. | point of division |
| It is called an__________ if the point of division lies on the given line segment and ____________ if the point of division lies on its extension | internal division; external division |
| A Midpoint is a special type of _____ point of division. It divides the line segment into two equal parts | internal |
| Note in equation of line: Multiplying nonzero real number to the equation of a line will not affect the solutions to the equation Hence, they are equivalent on xy plane. That is, they have different form but represents the same line. | nonzero real number |
Created by:
samzz