You visited us 1 times! Enjoying our articles? Unlock Full Access!

Radical Axis

The length of...

Question

The length of the tangent from the radical centre of the three circles $x^{2} + y^{2} + a x + b y + c = 0$ $(r = 1, 2, 3, and c > 0)$ to one of the three circles is

\sqrt{a_{1} + b_{1} + c}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{c}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{a_{1} a_{2} a_{3} + b_{1} b_{2} b_{3}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\sqrt{c}$
$s_{1} : x^{2} + y^{2} + a_{1} x + b_{1} y + c = 0$
$s_{2} : x^{2} + y^{2} + a_{2} x + b_{2} y + c = 0$
$s_{3} : x^{2} + y^{2} + a_{3} x + b_{3} y + c = 0$
So, radical axis is $s_{1} - s_{2} = 0$
$(a_{1} - a_{2}) x + (b_{1} - b_{2}) y = 0$ ---(1)
and other radical axis is $s_{1} - s_{3} = 0$
$(a_{1}, - a_{3}) x + (b_{1}, - b_{3}) y = 0$ ---(2)
Let (h,k) is a radical centre then
L $=$ lenght of tangent $= \sqrt{h^{2} + k^{2} + a_{1} h + b_{1} k + c}$
from (1) & (2) y= 0, x= 0.
(0,0) is radical centre of given circles
so, $L = \sqrt{c}$

Suggest Corrections

Similar questions

Q. If each pair of equations

a_{1} x^{2} + b_{1} x + c_{1} = 0, a_{2} x^{2} + b_{2} x + c_{2} = 0

and

a_{3} x^{2} + b_{3} x + c_{3} = 0

has a common root, then show that
(i)

\frac{c_{1} a_{2} + c_{2} a_{1}}{c_{1} a_{2} - c_{2} a_{1}} + \frac{a_{1} a_{2} b_{3}}{a_{3} (a_{1} b_{2} - a_{2} b_{1})} = 0

(ii)

{(\frac{a_{1} b_{2} - a_{2} b_{1}}{a_{1} c_{2} - a_{2} c_{1}})}^{2} = \frac{a_{1} a_{2} c_{3}}{c_{1} c_{2} a_{3}}

Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b1),(a3,b3),(a4,b2},(a5,b2)} . Prove that R is neither one one nor onto

Q. If the lines represented by

a x^{2} + 2 h x y + b y^{2} = 0

are

u = a_{1} x + b_{1} y = 0

and

v = a_{2} x + b_{2} y = 0

and are coinciding then:
(a)

\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}

(b)

\frac{a_{1}}{b_{1}} \neq \frac{a_{2}}{b_{2}}

(c)

a_{1} a_{1} = b_{1} b_{1}

(d)

a_{1} a_{1} + b_{1} b_{1} = 0

Q. If the equation of the locus of point equidistant from the points

(a_{1}, b_{1})

and

(a_{2}, b_{2})

(a_{1} - a_{2}) x + (b_{1} - b_{2}) y + c = 0,

then

c =

Q. If

2 y - x = 8; 5 y - x = 14, y - 2 x = 1

intersect at

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

Find

(a_{1} + a_{2} + a_{3} + b_{1} + b_{2} + b_{3})

Join BYJU'S Learning Program

The length of the tangent from the radical centre of the three circles x2+y2+ax+by+c=0 (r=1,2,3, and c>0) to one of the three circles is

The length of the tangent from the radical centre of the three circles $x^{2} + y^{2} + a x + b y + c = 0$ $(r = 1, 2, 3, and c > 0)$ to one of the three circles is