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The locus of a point, whose abscissa and ordinate are always equal is _______
Let co-ordinate of the point is . The abscissa of this point and co-ordinate.
So, the locus of the point is
The equation of straight line passing through the point \( (1,2) \) and parallel to the line \( y=3x+1 \) is_______
Now, required line is parallel to above line. So, slope
Hence, equation of requried line is
What can be said regarding if slope of a line is negative?
Given slope is negative
is a obtuse angle.
The equation of the line which cuts off equal and positive intercepts from the axes and passes through the point \((\alpha, \beta) \) is_____
Equation of line in intercept form is ,
But it passes through ,
Put the value in equation (i) is
Two lines \( a_1x+_1y+c_1=0 \) and \( a_2x+b_2y+c_2=0 \) are coincidence if _____
if , then and are coincidence.
Two lines \(L_1: a_1x+b_1y+c_1=0 \) and \( L_2: a_2x+b_2y+c_2=0 \) are parallel if _____
The equation of the line passing through the point \((2 , 3) \) with slope \( 2 \) is_____
Given the point and slope of the line is .
( Slope- point form)
The slope of the line \( ax+by+c=0 \) is_______
Equation of the line passing through \( (0,0) \) and slope \( m \) is_______
is equation of the line.
The angle between the lines \( x-2y =5 \) and \( y-2x=5 \) is______
Given line are (i)
In \( \triangle ABC \), if \( A \) is the point \((1, 2) \) and equation of the medians through \( B \) and \( C \) are respectively \( x+y=5 \) and \(x=4 \), then \( B \) is_____
Equation of the median through is . Let coordinates of are .
Now is median throught , so coordinates of i.e., midpoint of are
Now, this lies on
Two lines are perpendicular if the product of their slopes is______
\(y \)-intercept of the line \(4x-3y+15=0 \) is______
\(x \)-intercept of the line \(7x-9y+35=0 \) is______
The equation of the line passing through the points \( (1, 5) \) and \((2,3) \) is______
Given and be two points.
Now, equation of the line is
The length of the perpendicular from origin to a line is \( 7 \) and the line makes an angle of \( 150^o \) with positive direction of the \( y \)-axis . Then the equation of line is ______
Now, equation of line is
The sum of squares of the distances of a moving from two fixed points\( (a , 0) \) and \( (-a ,0) \) is equal to \( 2c^2 \) then equation of its locus is_____
Let be any position of the moving point and and be given points. Then
The equation of the locus of a point equidistance from the point \(A (5 ,9) \) and \( B(-3,4) \) is_______
Let be any point on the locus then
Hence, the locus of is
Find the Co-ordinate of the Centroid of triangle whose vertices are \( ( 3, -2) , (-2,3) \) and \( (-5, -3) \).
Coordinate of Centroid is
Let and are vertices of .
Find the incentre of the triangle ABC whose vertices are \( A( 0,3) , B (4, 0) \) and \( C ( 0,0 ) \).
In \( \triangle ABC , m < ABC=125^o \), then the circumcentre \( ( O ) \) of \( ABC \) lie_____
Hence be an obtuse triangle then the circumcentre lie outside the triangle.
In a triangle \( ABC \), the coordinate of orthocenter \( (H) \) is \( (4, 5) \) and circumcentre \( (O) \) is\(( -2, -3) \), then coordinate of centroid is______
be any triangle whose and , Centroid , Orthocentre and Circumcentre line in a straight line where divides in ratio.
Find the value of \( x \) if the distance between the points \( ( x , 8) \) and \( ( 4,3) \) is \( 13 \).
Find the coordinates of points which trisects the line segments joining \( ( 2, -3) \) and \( ( 4, 5) \).
The points of trisection are
Find the ratio in which the line joining the points \( A ( 1, 2) \) and \( B (-3 ,4) \) is divided by the line \(x+y-5=0 \)
Let the line divides in ratio at
Since lies on
Required ratio is externally.