Question

Find the co-ordinates of the middle point of the chord which the circlex2 + y2 + 4x – 2y – 3 = 0 cuts off the line x – y + 2 = 0.

Solution

Correct option is

λ = –1

 

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 

∴                      λ = –1.

                                                               

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

Find the equation of the circle which touches the axes and whose centre lies on the line x – 2y = 3.

Q4

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

Q5

A circle of radius 5 units touches the co-ordinates axes in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in the new position.

Q6

 

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

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

Q7

 

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

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

Q8

Find the points of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.

Q9

Find the length of the intercept on the straight line 4x – 3y – 10 = 0 by the circle x2 + y2 – 2x + 4y – 20 = 0.

Q10

For what value of λ will the line = 2x + λ be a tangent to the circle x2 +y2 = 5?