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The locus of a point, whose abscissa and ordinate are always equal is _______
Let coordinate of the point is . The abscissa of this point and coordinate.
Given that
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_______
Given
Slope
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?
Slope
Given slope is negative
when
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 ,
Given
(i)
But it passes through ,
(ii)
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 _____
when
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_______
Given
Slope
Equation of the line passing through \( (0,0) \) and slope \( m \) is_______
(Slopepoint form)
Hence
is equation of the line.
The angle between the lines \( x2y =5 \) and \( y2x=5 \) is______
Given line are (i)
and (ii)
From (i)
From (ii)
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
coordinates of
Two lines are perpendicular if the product of their slopes is______
Let slope
Slope of
\(y \)intercept of the line \(4x3y+15=0 \) is______
Given ,
intercept
\(x \)intercept of the line \(7x9y+35=0 \) is______
Given,
intercept
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 ______
Here,
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 Coordinate of the Centroid of triangle whose vertices are \( ( 3, 2) , (2,3) \) and \( (5, 3) \).
Coordinate of Centroid is
Let and are vertices of .
Hence
Find the incentre of the triangle ABC whose vertices are \( A( 0,3) , B (4, 0) \) and \( C ( 0,0 ) \).
Here
In \( \triangle ABC , m < ABC=125^o \), then the circumcentre \( ( O ) \) of \( ABC \) lie_____
In .
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 \( 13 \).
Let
Find the coordinates of points which trisects the line segments joining \( ( 2, 3) \) and \( ( 4, 5) \).
Here
and
Hence
and
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 \(x+y5=0 \)
Let the line divides in ratio at
Since lies on
Required ratio is externally.