CameraIcon

SearchIcon

MyQuestionIcon

1

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

Equation of Radical Axis

Find the equa...

Question

Find the equation of radical axis of two circle $x^{2} + y^{2} - 4 x - 2 y = 4$ and $x^{2} + y^{2} - 12 x - 8 y = 12.$

A

$4 x + 3 y + 4 = 0$

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

B

$4 x - 3 y - 4 = 0$

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

C

$4 x - 3 y + 4 = 0$

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

D

$3 x + 4 y - 4 = 0$

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

Open in App

Solution

The correct option is A
$4 x + 3 y + 4 = 0$

Radical axis of two circles is the locus of points whose powers with respect to the two circles are equal.
OR
we can say it is the locus of points at which tangents drawn to both circles have the same length.
Equation of radical axis of the two circles $S_{1} = 0 & S_{2} = 0$ is given by

$S_{1} - S_{2} = 0$

Here, $S_{1}$ is $x^{2} + y^{2} - 4 x - 2 y - 4 = 0$

$S_{2}$ is $x^{2} + y^{2} - 12 x - 8 y - 12 = 0$

Equation of the radical axis is

$S_{1} - S_{2} = 0$

$x^{2} + y^{2} - 4 x - 2 y - 4 - (x^{2} + y^{2} - 12 x - 8 y - 12) = 0$

$x^{2} + y^{2} - 4 x - 2 y - 4 - x^{2} - y^{2} + 12 x + 8 y + 12 = 0$

$8 x + 6 y + 8 = 0$

$4 x + 3 y + 4 = 0$

Equation of radical axis is $4 x + 3 y + 4 = 0$

Option A is correct

Suggest Corrections

thumbs-up

0

Similar questions

Q. Find the co - ordinates of the circles

x^{2} + y^{2} - 4 x - 2 y = 4

x^{2} + y^{2} - 12 x - 8 y = 12

touch each other. Also find equations of common tangents touching the circles in distinct points.

C_{1} = x^{2} + y^{2} - 4 x - 8 y - 5 = 0

C_{2} = x^{2} + y^{2} - 12 x - 2 y + 12 = 0

are the equations of two given circles. The equation of the circle on the common chord

P Q

as diameter is:

Q. Find the equation of the radical axis of the circle

x^{2} + y^{2} - 3 x - 4 y + 5 = 0

3 x^{2} + 3 y^{2} - 7 x - 8 y + 11 = 0

Q. The external centre of similitude of the circles

x^{2} + y^{2} - 12 x + 8 y + 48 = 0

x^{2} + y^{2} - 4 x + 2 y - 4 = 0

C_{1} = x^{2} + y^{2} - 4 x - 8 y - 5 = 0

C_{2} = x^{2} + y^{2} - 12 x - 2 y + 12 = 0

are the equations of two given circles. The length of the common chord of

C_{1}

C_{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Radical Axis of Two Circles

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Equation of Radical Axis

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon