If The Two Lines  cut The Co-ordinate Axes In Concyclic Points, Prove That a1a2 = b1b2 and Find The Equation Of The Circle.

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.



If the two lines  cut the co-ordinate axes in concyclic points, prove that a1a2 = b1b2 and find the equation of the circle.


Correct option is


The equation of any curve passing through 




Where λ is a parameter.

This curve will represent a circle. If the coefficient of x2 = coefficient of y2,  


and if the coefficient of xy = 0  

then                 a1b2 + a2b1 + λ = 0 


Substituting the value of λ in (1) then

From (2), b1b2 = a1a2  

∴ Equation of required circle is




The circle x2 + y2 – 4x – 8y + 16 = 0 rolls up the tangent to it at  by 2 units, assuming the x-axis as horizontal, find the equation of the circle in the new position.  



Find the equation of the circle of minimum radius which contains the three circles 

                   x2 – y2 – 4y – 5 = 0 

               x2 + y2 + 12x + 4y + 31 = 0  

and         x2 + y2 + 6x + 12y + 36 = 0


Find the equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius.



If the line x cos α + y sin α = p cuts the circle x2 + y2 = a2 in M and N, then show that the circle, whose diameter is MN, is 



A line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB. If the distance of the points A and B from the tangent at O, the origin, to the circle are m and n respectively, find the equation of the circle.


Tangents PQPR are drawn to the circle x2 + y2 = 36 from the point P(–8, 2) touching the circle at QR respectively. Find the equation of the circumcircle of the âˆ†PQR.


Let 1 and C2 be two circles with C2 lying inside C1. A circle C lying inside C1 touches C1 internally and C2 externally. Identify the locus of the centre of C.


The circle x2 + y2 – 4x – 4y + 4 = 0 is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circumcentre of the triangle is x + y – xy + k(x2 + y2)1/2 = 0. Find k.


Tangents TP and TQ are drawn from a point T to the circle x2 + y2 = a2. If the point T lies on the line px + qy = r, find the locus of centre of the circumcircle of triangle TPQ.