Question

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

Solution

Correct option is

± 5

 

Comparing the given line with y = mx + c, we get

m = 2, c = λ and given circle with x2 + y2 = a2

then                       a2 = 5

∵ Condition for tangency is

                 

                 λ2 = 25

∴               λ = ± 5.

SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

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.

Q4

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.

Q5

 

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

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

Q6

 

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

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

Q7

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

Q8

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

Q9

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.

Q10

Find the equation of tangent to the circle x2 + y2 – 2ax = 0 at the point