CircleHard
Question
A variable circle is drawn to touch the x-axis at the origin. The locus of the pole of the straight line lx + my + n = 0 w.r.t. the variable circle has the equation
Options
A.x(my - n) - ly2 = 0
B.x(my + n) - ly2 = 0
C.x(my - n) + ly2 = 0
D.none
Solution
Equation of variable circle which touch the x-axis at origin is
x2 + y2 + λy = 0
Let the pole of the above circle be P(h, k)
Equation of polar is
hx + ky +
(y + k) = 0
hx + (k +
) y + 
= 0 .....(1)
and the equation of given polar is
x + my + n = 0 .....(2)
comparing (1) and (2)
⇒ mh = lk +
and nh = 
⇒ mh = + lk +
⇒ mhk = lk2 + nh
∴ x(my - n) - ly2 = 0
x2 + y2 + λy = 0
Let the pole of the above circle be P(h, k)
Equation of polar is
hx + ky +
(y + k) = 0hx + (k +
) y + = 0 .....(1)and the equation of given polar is
x + my + n = 0 .....(2)
comparing (1) and (2)
⇒ mh = lk +
and nh = ⇒ mh = + lk +
⇒ mhk = lk2 + nh∴ x(my - n) - ly2 = 0
Create a free account to view solution
View Solution FreeMore Circle Questions
If the circle x2 + y2 = a2 intersects the hyperbola xy = c2 in four points P(x1, y1), Q(x2, y2), R(x3, y3), S(x4, y4), t...Line 3x + 4y = 25 touches the circle x2 + y2 = 25 at the point-...The centres of the circles x2 + y2 _ 6x _ 8y _ 7 = 0 and x2 + y2 _ 4x _ 10y _ 3 = 0 are the ends of the diameter of the ...The equation to a circle with centre (2, 1) and touching x axis is -...If r represent the distance of a point from origin & θ is the angle made by line joining origin to that point from ...