A conic section is a curve formed by the intersection of a plane and a double-napped cone. The four main types are circles, ellipses, parabolas, and hyperbolas, each with distinct properties and equations.
Mathematics Notes For Class 12 Chapter 6
A function which is to be maximized or minimized is called an: Objective function
The ordered pair ____________ is a solution of the inequality x + 2y < 6: (1, 1)
ax < b is an inequality of: One variable
(1, 0) is not solution of inequality: x – 3y < 0
The graph of the inequality ax+by<c is: Half plane
Point (1, 2) lies in the region of inequality: 2x + y < 5
The graph of 2x + y > 2 is the open half plane the region is _______ the origin side of 2x + y = 2: Not on
ax + b < c is an inequality of one variable: One variable
If ax+by: Associated equation
The inequality y < b is the open half plane to the __________ of the boundary line y = b: Below
(0,1) is not the solution of inequality: x +3y < 0
If the segment obtained by joining any two points of a region lies entirely with in the region, then the region is called: Convex
The linear equation __________ is called the associated or corresponding equation of the inequality ax + by > c: ax + by = c
(-2, 3) lies in the solution region of: x + 3y > 5
(1,0) is in the solution of inequality: 3x +5y < 7
ax+b<0 is an: Inequality
ax + b < c is linear inequality in: one variables
The operation __________ a constant to each side of inequality will not effect the order (or sense) of inequality: Subtracing
The feasible solution, which maximizes or minimizes the objective function, is called the: Optimal solution
The inequality 2x + 3y < 5 is satisfied by point: (-2, 1)
The feasible region is _______ if it cannot be enclosed in a circle: Unbounded
If a function f(x, y) have same minimum value at any two points, then it is ___________ at all the points of the line segment between these points: Minimum
The point (-1, 2) satisfied the inequality: x + y < 4
The system of linear inequality concerning the problem is named as problem: Constaint
y = b is a horizontal line perpendicular to: y-axis may be
If r = 0 then x2 + y2 = r2 is called ————— circle: Point
The inequality y > b is the closed half plane to the ________ of the boundary line y = b: Above
For inequalities 2x + y < 10 and x + 4y < 12, the corner point: (4, 2)
x = a is a vertical line perpendicular to: x-axis
ax+b>0 is an: Inequality
The non-negative constraints are called: Decision variables
The order (or sense) of an inequality is change by ____________, it each side by a negative constant: Dividing
The order of sense of an inequality is change by _________ it each side by a negative constant: Multiplying
(0,1) is in the solution of inequality: x +y < 2
2x -7y > 3 is linear inequality in: two variable
A point (x,y) which satisfy a linear inequality in teo variables x & y form its: Solution
(3,2) is not in the solution of inequality: x +y ? 1
The feasible solution which maximum or minimize the objective function is called the: Feasible solution
(1, 0) is the solution of inequality: 3x + 5y < 6
Medians of a triangle are: Concurrent
x = 0 is not in the solution of inequality: x + 4 > 0
The end points of major axis of ellipse are called: vertices
ax = by < c is an inequality of two variables: Two variable
ax+by+c > 0 is an: Inequality
The centre of the circle (x – 5)2 + (y-3)2 = 8 is: (5, 3)
ax + by > c is an inequality of: Two variable
ax < b is an inequality of one variable: One variable
The region of the graph ax + by < c is called ___________ half plane: Open
There are _______ ordered pairs that satisfy the inequality ax + by > c: Infinitely many
An expression involving anyone of the symbols < (less than), > (greater, then) ? (less then or equal to), ? greater than or equal to) is called: inequality
ax + by > c is an inequality of two variables: Two variable
A vertical line line divides the plane into _________ half planes: Left and Right
A quadrilateral having two parallel and two non-parallel sides, is called: Trapezium
Ax2 + By2 + Gx + Fy + C = 0 form hyperbola if: A
x = – 5 is in the solution of: 2x + 3 < 0
The region of the graph ax + by > c is called _________ half plane: Closed
The focus of parabola y2 = -8x is: (-2, 0)
A function which is to be maximized or minimized is called an: Objective function
(0, 0) is the in the solution of inequality: 3x + 5y > 7
If a function f(x, y) have same maximum value at any two points, then it is _________ at all the points of the line segment between these point: Maxnimum
A vertical line divides a plane into ______ half planes: Left and right
There are _________ ordered pairs that satisfy the inequality ax + by < c: ax + by = c
The operation ________ by a positive constant to each side of inequality will not effect the order (or sense) of inequality: Dividing
There are ___________ ordered pairs that satisfy the inequality ax + by < c: Infinitely many
(2,1) is one of the solutions of the inequality: 2x+y<7
x = 4 is the solution of inequality: x + 3 > 0
If e = 0, then conic is called: circle
The solution of ax + by ? c is: closed half plane
x = c is a vertical line parallel to: y-axis
The inequality y > b is the open half plane to the _________ of the boundary line y = b: Above
A point does not lie in the feasible region is ________ corner point of the feasible region: Not a
Altitudes of a triangles are: Concurretn
Two non-parallel lines interest each other at: Only one point
The graph of linear equation of the form ax + by = c is a ___________ , where a, b and c are constants and a, b are not both zero: Straight line
There are _________ feasible solution in the feasible region: Infinitely many
(1,3) is one of the solutions of the inequality: 3x+5y>29
ax + b > c is an inequality of one variable: One variable
The graph of 2x + y < 2 is the open half plane the region is _________ the origin side of 2x + y = 2: On
y = b is a horizontal line perpendicular to: y axis may be
The inequality x < a is the closed half plane to the _________ of the boundary line x = a: Left
x = 01 is solution of inequality: 2x + 3 > 0
Most general form of 2nd degree ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 form a circle if: h2 – ab < 0
An expression involving any of the symbols <,> or: Inequality
The region of the graph ax + by = c is called the _______ half planes ax + by < c and ax + by < c: Boundary of
The feasible region is __________ if it can easily be enclosed within a circle: Bounded
Which one is a solution of inequality 2x + 3y < 0: (-1, -2)
The associated equation of inequality x + 2y < 6 is: x + 2y = 6
The graph of the inequality ax + by < c is: Half plane
The graph of 2x + y > 2 is the closed half plane the region is _________ the origin side of 2x + y =2: Not on
x + 2y > 6 is not satisfied by: (2, 2)
The solution region restricted to 1st quadrant is: Feasible region
The system of ______________ involved in the problem concerned is called problem constraints: Linear inequalities
x = 0 is the solution of the inequality: 2x + 1 > 0
The line through focus and perpendicular to directrix of parabola is called: Axis of Parabola
Ax2 + By2 + Gx + Fy + C = 0 form ellipse if: A
A point of a solution region where two of its boundary lines intersects is called a ___________ of the solution region: Vertex
The region of the graph ax + by < is called __________ half plane: Closed
The point (1, 2) satisfies inequality: x + 2y > 3
x = -3 is the solution of the inequality: 2x – 1 < 0
(0,0) is one of the solutions of the inequality: 2x+3y<5
Important : Review all previous years’ 12 Class Past Papers for comprehensive practice and better exam preparation.