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.

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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

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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

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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

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Q6

 

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

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Q7

 

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

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Q8

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Q9

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Q10

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