“Explore the basics of Analytic Geometry, which combines algebra and geometry to study shapes, lines, and curves using coordinate systems and equations.”
Important questions of Chapter 4 Mathematics Class 12
Equation of horizontal line through (a, b) is: x = b
The point of concurrency of medians of triangle is called: Centroid
y = c a line: Perpendicular to y-axis
The distance of the point (-2, 3) from y-axis is: 1
The centroid of a triangle is a point that divides each median in the ratio: 2:01
If a=0 then ax+by+c=0, shows that line is: Parallel to x-axis
The distance of a point P(x,y) from origin is: ?(x2+y2 )
Point-slope form of equation of a straight line: y-y1=m(x-x1)
If x<0, y<0 then the point P(x,y) lies in the quadrant: 3rd
The equation of a straight line which parallel to the line 3x – 2y + 5 = 0 and passes through (2, -1) is: 3x – 2y – 8 = 0
If a,b,c are in A.P., then the line ax + by + c = 0 will always pass through a fixed point whose co-ordinates are given by: (1, -2)
The pair of lines of homogenous second degree equation ax2+ 2hxy + by2= 0 are real and distinct, if: h2> ab
Equation of X-axis is: y = 0
The equation of the straight line which passes through the point (1, -3) and makes an intercept on the y-axis twice as long as that on the x-axis is: 2x + y +1 = 0
The point of concurrency of the angle bisectors of a triangle is called its: Centroid
A linear equation in two variables represent a: Stranght line
If x>0, y>0 then the point P(x,y) lies in the quadrant: 1st
The point where the altitudes of a triangle meet each other is called: orthocentre
The point P(x1, y1) lies ——— the line ax + by + c = 0 if ax1 + by1 + c < 0: below
The extremities of a diagonal of a parallelogram are the points (3, 4) and (-6, 5), if third vertex is (-2, 1) then fourth vertex is: (1, 1)
The ratio in which the line segments joining (2, 3) and (4,1) is divided by the line joining (1, 3) and (4, 3) is: 1:03
The distance of the point (2,3) from x-axis is: 3
Distance of (-3, 7) from x-axis is: 7
If a linelis parallel to x-axis then slope is: ?
Length of perpendicular from (0, 0) to line 4x – 3y – 1 = 0 equals: 5
The distance of a point P(2,1) form origin is: ?5
The points (-a, -b), (0, 0), (a, b) and (a2, ab) are: Collinear
Equation of x-axis is: y=0
X-co-ordinate of centroid of triangle ABC with A(-2, 3), B(-4, 1),C(3, 5) equals: 3
If m1 & m2 are slopes of two parallel lines then: m1
If m1 & m2 are slopes of two perpendicular lines then: m1m2 = -1
A French mathematician introduced algebraic methods in geometry named: Rene Descartes
If a>0 & y=a, then the line l is: Above the x-axis
The distance between (2,1) & (-3,5) is: ?41
Slope of y-axis is: Undefined
If b>0 & x=b, then the line l is: On the right of the y-axis
Any line perpendicular to the line ax + by + c = 0 is: bx – ay = c’ = 0
The distance of 12x + 5y = 7 from origin is: 13-Jul
The ratio in which y-axis divides the line joining (2, -3) and (-5, 6) is: 1:02
The coordinate axes divide the plane into __________ equal parts: 4
If a<0 & y=a, then the line l is: Below the x-axis
The ordered pair (x,y) gives us enough information about the: Location of the point P
x is negative and y is positive in: Fourth quadrant
Slope-intercept form of equation of a straight line: y=mx+c
The point of intersection of medians of a triangle is called: centroid
If the point P(x1, y1) lies on l,then the distance d would be: 0
If (2,4)(4,6)&(3,5) are the vertices of a triangle then its centroid is: (3,5)
The point of intersection of median of a triangle is: Centroid
When a line intersects the y-axis at (0, 4) then y-intercept is: 4
Intercept form of equation of a straight line: x/a + y/b =1
The popint A(x1,y1) is above the line ax+by +c=0, b > 0: ax1 +by1 +c > 0
If distance of a point P(x,y) from origin is 7 then: ?x2+y2 =7
The two lines a1x+b1y+c1 = 0 and a2x+b2y+c2 intersect each other if: a1b1 -n1a2 ? 0
If distance of a point P(x,y) from x-axis is 3 then: y=3
The angle between the lines x/?3+y = 1 and x/?3 -y = 1 is: 60°
In a plane two mutually perpendicular lines are called: Coordinate axes
The distance of a point P(-3,-5) from y-axis is: 3
If A,B,C are three points such that slope of AB = slope of AC then: Points are collinear
For all values of a and b the line (a + b)x + (a – b)y = 2a + 3b passes through the fixed point: (5/2 , -1/2)
If slope of Ab = AB = slope of AC, them the points A,B and C are: Coplanar
The point P in the plane that corresponds to an ordered pair (x,y) is called: Graph of (x,y)
If (2,3)(5,4)&(3,7) are the vertices of a triangle then its centroid is: (10/3, 14/3)
If a non-vertical linel with inclination: Tan
If m is slope of line passing through origin then its equation is: y = mx
Point of intersection of lines x – 2y + 1 = 0 and 2x – y + 2 = 0 equals: (1, 0)
If A and B are the points (-3, 4) and (2, 1) then the coordinates of the point C and AB produced such that AC = 2BC are: (7, -2)
if (x,y) are the coordinates of a point P,then the second component of this ordered pair is called: Ordinate
If b<0 & x=b, then the line l is: On the left of the y-axis
x and y both are positive in: First quadrant
If a point P(x,y) is on y-axis then: x=0
The distance of a point P(-2,-3) from x-axis is: 3
The distance of a point P(x,y) from x-axis is: |y|
In translation of axex, origin is shifted but axes remain ————– to the old axes: parallel
The line l is horizontal if and only if slope is equal to: 0
If A (-3,6) and B(3,2), then slope of AB is: 3-Feb
The vertical line y’oy is called: Y-axis
The centroid of a triangle divides each median in the ratio: 3:01
x = c is a line: Perpendicular to x-axis
The equation to the straight line which passes through the point (2, 9) and makes an angle of 45 degree with x-axis is: x – y + 7 = 0
If A(x1,y1) & B(x2,y2) then ?((x1-x2)2)+(y1-y2)2 is called: Distance formula
If (3, 1) & (5, 1) are the end points of diameter of a circle of a circle then coordinates of its center are: (4, 1)
Two non-parallel lines in a plane intersect each other at: One and only one point
The point of intersection of angle bisectors of a triangle is called: In centre
if (x,y) are the coordinates of a point pthen the first component of this pair is called: abscissa
Two lines a1x+ b1y + c1 0 and a2x b2y + c2 = 0 are parallel if and only if: a1/a2 =b1/b2
If m1= m2, then both lines will be: Parallel
General form of equation of line is: ax + by + c = 0
Mid point of A(2, 0), B(0, 2) is: (1, 1)
The x-intercept of the line 2x + 3y – 1 = 0 is: 3
If two lines with slopes m1and m2are parallel, then: m1m2= 0
The centroid of a: 2:01
Centroid is a point which divides each median in: 2:01
The value of m so that the lines 3x + y + 2 = 0, 2x – y + 3 = 0 and x + my – 3 = 0 may be concurrent is: m = 4
If (3, -4) and (-6, 5) are the extremities of the diagonal of a parallelogram and (-2,1) is third vertex, then its fourth vertex is: (-1, 0)
If x=0 then the point P(x,y) is on: y-axis
In a plane two mutually perpendicular numbered lines intersect at: Origin
Equation of a line parallel to y-axis is: x = a
If distance of a point P(2,2) from the origin: ?8
The line x = a is on the right of y – axis if: a > 0
Two non parallel lines intersect each other at: 1 point
Important : Review all previous years’ 12 Class Past Papers for comprehensive practice and better exam preparation.