Question

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

Solution

Correct option is

 

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 

              

              

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 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  

               

                

Q3

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.

Q4

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.

Q5

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. 

Q6

 

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

Q9

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.   

Q10

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