lines are perpendicular. Coordinate Geometry Solution Equation of the straight line, parallel to is k Since it passes through the point ( , ) + k = k = = Therefore, equation of the required straight line is Example . Find the equation of a straight line perpendicular to the line y and passing through the point ( , – ) . Solution The equation y can be written as Equation of a straight line perpendicular to is k Since it is passes through the point ( , – ) , + k = we get, k = − Therefore, equation of the required straight line is Example .
Find the equation of a straight line parallel to Y axis and passing through the point of intersection of the lines and x . Solution Given lines = ... ( ) = ... ( ) To find the point of intersection, solve equation ( ) and ( ) = − = − - = − = − x = , y = Therefore, the point of intersection ( , ) x y = The equation of line parallel to Y axis is x = c .
It passes through ( , ) x y = . Therefore, c = . The equation of the line is x = ⇒ x − Example . The line joining the points A ( , ) and B ( , ) is a tangent to a circle whose centre C is at the point ( , ) find (i) the equation of the line AB .
(ii) the equation of the line through C which is perpendicular to the line AB . (iii) the coordinates of the point