Question

Find the coordinates of the middle point of the chord which the circle x2y2 + 4x – 2y – 3 = 0 cut off the line x – y + 2 = 0.   

Solution

Correct option is

 

Centre and radius of the circle x2 + y2 + 4x – 2y – 3 = 0 are (–2, 1) and  respectively.  

Draw perpendicular from O upon x – y + 2 = 0 is OM 

Equation of OM which is perpendicular to x – y + 2 = 0 is x + y = λ, it passes through (–2, 1)

Then            –2 + 1 = λ   

  

Then equation of OM in x + y + 1= 0 

Since M is the midpoint of PQ which is point of intersection of

x – y + 2 = 0 and x + y +1 = 0, coordinates of M is      

SIMILAR QUESTIONS

Q1

Find the equation of circle passing through the three non-collinear points (1, 1), (2, –1) and (3, 2).

Q2

Find the equation of the circle whose diameter is the line joining the points (–4, 3) and (12, –1). Find also the intercept made by it on y axis.

Q3

 

Find the equation of circle which touches axis of y at a distance 4 units from the origin and cuts the intercept of 6 units from the axis of x.

Equation of circle in intercepts  

               

                

Q4

Find the equation of the circle which passes through the origin and makes intercepts of length a and b on axis of x and y respectively.

Q5

A circle of radius 2 lies in the first quadrant and touches both the axes of coordinate. Find the equation of circle with centre at (6, 5) and touching the above circle externally.

Q6

A circle of radius 5 units touches the coordinates axes in 1st quadrant. If the circle makes one complete roll on x axis along positive direction of xaxis. Find the equation in new position. 

Q7

 

Discus the position of the points (1, 2) and (6, 0) with respect to the circle.

                 x2 + y2 – 4x + 2y – 11 = 0   

Q8

 

Find the shortest and largest distance from the point (2, –7) to the circle 

                 x2 + y2 – 14x – 10y – 151 = 0   

Q9

Find the length of intercept on the S.L. 4x – 3y – 10 = 0 by the circle x2y2 – 2x + 4y – 20 = 0.

Q10

For what values of λ will the line y = 2x + λ be a tangent to the circle x2y2 = 5.