30 Questions
What is the general form of a linear equation in two variables x and y?
ax + by + c = 0
What is the solution of the linear equation x + y = -b?
y = -bx - b
What does the graph of a linear equation in two variables represent?
A line
What is the ratio of the change in y-direction to the change in x-direction?
Slope
What is the definition of a linear equation in two variables?
An equation of the form ax + by + c = 0
What is the solution of the linear equation y = -bx - b?
x = -b
What is the condition for the existence of a solution to a pair of simultaneous linear equations?
The equations represent two non-parallel lines
What is the value of x1 and y1 in the solution to the pair of simultaneous linear equations?
x1 = bc1/ab2 - bc2/ab1, y1 = bc2/ab2 - bc1/ab1
What is the method used to solve the equations in the example given?
Elimination method
If the equations are multiplied by certain multiples of coefficients, what is the purpose of doing so?
To eliminate either x or y
What is the condition for the slopes of the two lines to be unequal?
a1/b1 ≠ a2/b2
What is the purpose of solving simultaneous linear equations?
To find the point of intersection of two lines
What is the shape of the surface generated by rotating the line 𝑚𝑚 around the line 𝑙𝑙 with a constant angle 𝛼𝛼?
Double napped right circular hollow cone
What is the section obtained when a plane intersects a cone at an angle 𝛽𝛽 equal to 90°?
Circle
What is the fixed point called in a circle?
Centre
What is the distance from the centre to a point on the circle called?
Radius
What is the equation of the circle in Cartesian coordinates?
𝑥𝑥 − ℎ 2 + 𝑦𝑦 − 𝑘𝑘 2 = 𝑟𝑟
What is the shape of the section obtained when a plane intersects a cone at an angle 𝛽𝛽 less than 𝛼𝛼?
Hyperbola
What is the equation of a point in polar coordinates?
x = r cos θ + h
What is the definition of an ellipse?
The set of all points in a plane, the sum of whose distances from two fixed points is a constant.
What is the middle point of the line segment joining the foci of an ellipse called?
Centre
What is the line segment through the centre and perpendicular to the major axis of an ellipse called?
Minor axis
In the equation of an ellipse, what does 'a' represent?
Half the length of the major axis
What is the sum of the distances of a point on an ellipse to the foci?
2a
What is the sum of the distances from the point P to the foci in an ellipse?
2(𝑏𝑏2 + 𝑐𝑐2)
What is the value of 𝑎𝑎 in terms of 𝑏𝑏 and 𝑐𝑐?
√(𝑏𝑏2 + 𝑐𝑐2)
What is the definition of eccentricity 𝑒𝑒 of an ellipse?
𝑐𝑐 / 𝑎𝑎
What is the equation of the ellipse in terms of 𝑥𝑥 and 𝑦𝑦?
𝑥𝑥2 / 𝑎𝑎2 + 𝑦𝑦2 / 𝑏𝑏2 = 1
What is the value of 𝑐𝑐 in terms of 𝑎𝑎 and 𝑏𝑏?
√(𝑎𝑎2 - 𝑏𝑏2)
What is the foci of the ellipse in the coordinate plane?
F1(−𝑐𝑐, 0), F2(𝑐𝑐, 0)
Test your understanding of linear equations in two variables, including their definitions, solutions, and graphing. Learn how to solve linear equations and find the unique values of y for every value of x.
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