Advertisements
Advertisements
Question
Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)
Advertisements
Solution
The distance between the line ax + by + c = 0 and the point (x1, y1) is d = `("a"x_1 + "b"y_1 + "c")/(sqrt("a"^2 + "b"^2)`
Here (x1, y1) = (−2, 4) and the equation of the line is 4x + 3y + 4 = 0
∴ Required dostance = `(4(- 2) + 3(4) + 4)/sqrt(4^2 + 3^2)`
= `(- 8 + 12 + 4)/(sqrt(16 + 9)`
= `8/5`
APPEARS IN
RELATED QUESTIONS
Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0
Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6
If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Find the family of straight lines perpendicular
Find the family of straight lines parallel to 3x + 4y – 12
A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units
A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Find the cost of making 40 copies
Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers
Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers
Choose the correct alternative:
The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are
Choose the correct alternative:
A line perpendicular to the line 5x − y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq.units, then its equation is
Choose the correct alternative:
The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is
Choose the correct alternative:
If the lines represented by the equation 6x2 + 41xy – 7y2 = 0 make angles α and β with x-axis then tan α tan β =
