Question

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

Solution

Correct option is

10

 

Centre and radius of the circle x2 + y2 – 2x + 4y – 20 = 0 are

(1,–2) and  respectively. 

Let OM be the perpendicular from O on the line 4x – 3y – 10 = 0

Hence line 4x – 3y – 10 = 0 passes through the centre of the circle.

Hence intercepted length = diameter of the circle

                                         = 2 × 5 = 10

SIMILAR QUESTIONS

Q1

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.

Q2

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.

Q3

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.

Q4

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

Q5

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.

Q6

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.

Q7

 

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

Q10

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.