Linear Equations in Two Variables

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What is the general form of a linear equation in two variables x and y?

ax + by - c = 0

ax + by = c

ax + by + c = 0 (correct)

ax - by + c = 0

What is the solution of the linear equation x + y = -b?

x = -b

x = -b, y = -b

y = -b

y = -bx - b (correct)

What does the graph of a linear equation in two variables represent?

A parabola

A circle

A curve

A line (correct)

What is the ratio of the change in y-direction to the change in x-direction?

Slope Signup and view all the answers

What is the definition of a linear equation in two variables?

An equation of the form ax + by + c = 0 Signup and view all the answers

What is the solution of the linear equation y = -bx - b?

x = -b Signup and view all the answers

What is the condition for the existence of a solution to a pair of simultaneous linear equations?

The equations represent two non-parallel lines Signup and view all the answers

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 Signup and view all the answers

What is the method used to solve the equations in the example given?

Elimination method Signup and view all the answers

If the equations are multiplied by certain multiples of coefficients, what is the purpose of doing so?

To eliminate either x or y Signup and view all the answers

What is the condition for the slopes of the two lines to be unequal?

a1/b1 ≠ a2/b2 Signup and view all the answers

What is the purpose of solving simultaneous linear equations?

To find the point of intersection of two lines Signup and view all the answers

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 Signup and view all the answers

What is the section obtained when a plane intersects a cone at an angle 𝛽𝛽 equal to 90°?

Circle Signup and view all the answers

What is the fixed point called in a circle?

Centre Signup and view all the answers

What is the distance from the centre to a point on the circle called?

Radius Signup and view all the answers

What is the equation of the circle in Cartesian coordinates?

𝑥𝑥 − ℎ 2 + 𝑦𝑦 − 𝑘𝑘 2 = 𝑟𝑟 Signup and view all the answers

What is the shape of the section obtained when a plane intersects a cone at an angle 𝛽𝛽 less than 𝛼𝛼?

Hyperbola Signup and view all the answers

What is the equation of a point in polar coordinates?

x = r cos θ + h Signup and view all the answers

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. Signup and view all the answers

What is the middle point of the line segment joining the foci of an ellipse called?

Centre Signup and view all the answers

What is the line segment through the centre and perpendicular to the major axis of an ellipse called?

Minor axis Signup and view all the answers

In the equation of an ellipse, what does 'a' represent?

Half the length of the major axis Signup and view all the answers

What is the sum of the distances of a point on an ellipse to the foci?

2a Signup and view all the answers

What is the sum of the distances from the point P to the foci in an ellipse?

2(𝑏𝑏2 + 𝑐𝑐2) Signup and view all the answers

What is the value of 𝑎𝑎 in terms of 𝑏𝑏 and 𝑐𝑐?

√(𝑏𝑏2 + 𝑐𝑐2) Signup and view all the answers

What is the definition of eccentricity 𝑒𝑒 of an ellipse?

𝑐𝑐 / 𝑎𝑎 Signup and view all the answers

What is the equation of the ellipse in terms of 𝑥𝑥 and 𝑦𝑦?

𝑥𝑥2 / 𝑎𝑎2 + 𝑦𝑦2 / 𝑏𝑏2 = 1 Signup and view all the answers

What is the value of 𝑐𝑐 in terms of 𝑎𝑎 and 𝑏𝑏?

√(𝑎𝑎2 - 𝑏𝑏2) Signup and view all the answers

What is the foci of the ellipse in the coordinate plane?

F1(−𝑐𝑐, 0), F2(𝑐𝑐, 0) Signup and view all the answers