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G Gautam harsolia
Given equation of line is we can rewrite it as Now, we know that In this problem A = 4 , B = 3 C = -12 and d = 4 point is on x-axis therefore   = (x ,0) Now, Now if x > 3 Then,   Therefore, point is (8,0)            and if x < 3 Then, Therefore, point is (-2,0) Therefore, the points on the x-axis, whose distances from the line    are    units are  (8 , 0) and (-2 , 0)

G Gautam harsolia
Given the equation of the line is we can rewrite it as Now, we know that         where A and B are the coefficients of x and y and  C is some constant  and   is point from which we need to find the distance  In this problem A = 12 , B = -5 , c = 82 and  = (-1 , 1) Therefore, Therefore, the distance of the point    from the line    is 5 units

G Gautam harsolia
Given equation is Coefficient of x is 1 and y is -1 Therefore,  Now, Divide both the sides by  we wiil get we can rewrite it as Now, we know that normal form of line is Where  is the angle between perpendicular and the positive x-axis and p is the perpendicular distance  from the origin On compairing equation (i) and (ii) we wiil get Therefore,  the angle between perpendicular...

G Gautam harsolia
Given equation is we can rewrite it as Coefficient of x is 0 and y is 1 Therefore,  Now, Divide both the sides by 1 we will get we can rewrite it as Now, we know that normal form of line is Where  is the angle between perpendicular and the positive x-axis and p is the perpendicular distance  from the origin On comparing equation (i) and (ii) we wiil get Therefore,  the...

G Gautam harsolia
Given equation is we can rewrite it as Coefficient of x is -1 and y is  Therefore,  Now, Divide both the sides by 2 we will get we can rewrite it as Now, we know that the normal form of the line is Where  is the angle between perpendicular and the positive x-axis and p is the perpendicular distance  from the origin On comparing equation (i) and (ii) we wiil get Therefore,  the...

G Gautam harsolia
Given equation is we can rewrite it as                           Therefore,  intercepts on y-axis are  and there is no intercept on x-axis

G Gautam harsolia
Given equation is we can rewrite it as                          -(i) Now, we know that the intercept form of line is                          -(ii) Where a and b are intercepts on x and y axis respectively On comparing equation (i) and (ii) we will get  and  Therefore,  intercepts on x and y axis  are  and -2 respectively

G Gautam harsolia
Given equation is we can rewrite it as                          -(i) Now, we know that the intercept form of line is                          -(ii) Where a and b are intercepts on x and y axis respectively On comparing equation (i) and (ii) we will get a = 4 and b = 6 Therefore,  intercepts on x and y axis  are 4 and 6 respectively

G Gautam harsolia
Given equation is                                   -(i) Now, we know that the Slope-intercept form of the line is                       -(ii) Where m is the slope and C is some constant On comparing equation (i) with equation (ii) we  will get   and  Therefore, slope and y-intercept are   respectively

G Gautam harsolia
Given equation is we can rewrite it as                             -(i) Now, we know that the Slope-intercept form of line is                       -(ii) Where m is the slope and C is some constant On comparing equation (i) with equation (ii) we  will get   and  Therefore, slope and y-intercept are   respectively

G Gautam harsolia
Given equation is we can rewrite it as                             -(i) Now, we know that the Slope-intercept form of the line is                       -(ii) Where m is the slope and C is some constant On comparing equation (i) with equation (ii) we  will get   and  Therefore, slope and y-intercept are   respectively

G Gautam harsolia
Points are collinear means they lies on same line Now,  given points are    and   Equation of line passing through point A and B is Therefore, the equation of line passing through A and B is  Now, Equation of line passing through point B and C is Therefore, Equation of line passing through point B and C is  When can clearly see that  Equation of line passing through point A nd B ...

G Gautam harsolia
Let the coordinates of Point A is (x,0) and of point B is (0,y) It is given that point R(h , k) divides the line segment between the axes in the ratio  Therefore, R(h , k)  Therefore, coordinates of point A is   and of point B is  Now, slope of line passing through points  and   is  Now, equation of line passing through point   and with slope  is  Therefore, the equation of line is

G Gautam harsolia
Now, let coordinates of point A is (0 , y) and of point B is (x , 0) The, Therefore, the coordinates of point A is (0 , 2b) and of point B is (2a , 0) Now, slope of line passing through points (0,2b) and (2a,0) is Now, equation of line passing through point (2a,0) and with slope    is Hence proved

G Gautam harsolia
It is given that the owner of a milk store sell 980 litres milk each week at  and    litres of milk each week at   Now, if we assume the rate of milk as x-axis and Litres of milk as y-axis Then, we will get coordinates of two points i.e.  (14, 980)  and   (16, 1220) Now, the relation between  litres of milk and Rs/litres is given by equation  Now, at  he could sell He could sell...

G Gautam harsolia
It is given that If  then  and  If    then   Now, if assume C along x-axis and L along y-axis Then, we will get coordinates of two points (20 , 124.942)  and (110 , 125.134) Now, the relation between C and L is given by equation Which is the required relation

G Gautam harsolia
Let the slope of the line is m and slope of a perpendicular line is which passes through the origin (0, 0) and (-2, 9) is Now, the slope of the line is Now, the equation of line passes through the point (-2, 9) and with slope   is Therefore, the equation of the line is

G Gautam harsolia
We know that  Now, equation of line passing through point (0 , 2) and with slope  is Therefore, equation of line is                   -(i) Now, It is given that line crossing the -axis at a distance of units below the origin which means coordinates are  (0 ,-2) This line is parallel to above line which means slope of both the lines are equal Now, equation of line passing through point...