# Find the radical axis of the pairs of circles ${x^2} + {y^2} - xy + 6x - 7y + 8 = 0$ and ${x^2} + {y^2} - xy - 4 = 0$ , the axes being inclined at ${120^ \circ }$

Last updated date: 15th Mar 2023

•

Total views: 304.8k

•

Views today: 4.84k

Answer

Verified

304.8k+ views

Hint: Make use of the equation of the radical axis of a pair of circles and solve this question

Let us consider the equation of the given two circles as ${S_1}$ and ${S_2}$.

Complete step-by-step answer:

So, we can write the equation of the first circle is given by

${S_1} = {x^2} + {y^2} - xy + 6x - 7y + 8 = 0$

The equation of the second circle is given by

\[{S_2} = {x^2} + {y^2} - xy - 4 = 0\]

Now, we know that the equation of the radical axis of a pair of circles ${S_1}$ and ${S_2}$ is given by

${S_1} - {S_2} = 0$

So, on doing ${S_1} - {S_2}$ , we get

${x^2} + {y^2} - xy + 6x - 7y + 8 - ({x^2} + {y^2} - xy - 4) = 0$

So, on solving this we get

6x-7y+12=0

Hence the equation of the radical axis is 6x-7y+12=0.

Note: In this question we have been asked to find out the equation of radical axis of a pair of circles , in case we have been asked to find out equation of some other form of a circle then apply the suitable formula and solve it accordingly

Let us consider the equation of the given two circles as ${S_1}$ and ${S_2}$.

Complete step-by-step answer:

So, we can write the equation of the first circle is given by

${S_1} = {x^2} + {y^2} - xy + 6x - 7y + 8 = 0$

The equation of the second circle is given by

\[{S_2} = {x^2} + {y^2} - xy - 4 = 0\]

Now, we know that the equation of the radical axis of a pair of circles ${S_1}$ and ${S_2}$ is given by

${S_1} - {S_2} = 0$

So, on doing ${S_1} - {S_2}$ , we get

${x^2} + {y^2} - xy + 6x - 7y + 8 - ({x^2} + {y^2} - xy - 4) = 0$

So, on solving this we get

6x-7y+12=0

Hence the equation of the radical axis is 6x-7y+12=0.

Note: In this question we have been asked to find out the equation of radical axis of a pair of circles , in case we have been asked to find out equation of some other form of a circle then apply the suitable formula and solve it accordingly

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE