Find The Locus Of The Pole Of The Line lx + my + n = 0 With Respect To The Circle Which Touches y-axis At The Origin.

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.



Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.


Correct option is

y(lx – n) = mx2


Let centre of circle be C(h, 0) since circle touches y-axis at the origin.

∴        Radius of the circle = h

∴ Equation of the circle 

                (x – h)2 + (y – 0)2 = h2

Let the pole be (x1y1

∴ Equation of the polar w.r.t circle (1) is 

                 xx1 + yy1 – h (x + x1) = 0

And given line lx + my + n = 0 which is (2):


From first two relations, we get


and from last two relations, we get





∴ Locus of pole is          y(lx – n) = mx2      








Show that the locus of the point, the powers of which with respect to two given circles are equal, is a straight line.



Find the condition that chord of contact of any external point

(hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle.


The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.


Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).


Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.


Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).


Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .


If two tangents are drawn from a point on the circle x2 + y2 = 50 to the circle x2 + y2 = 25 then find the angle between the tangents.



Find the equation of the diameter of the circle

x2 + y2 + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.


Examine if the two circles x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally.