The equation of a circle passing through the origin and cutting the given circles x2 + y2 + 2g1x + 2g1x + c1 = 0 and x2 + y2 + 2g2x + 2g2x + c2 = 0 orthogonally . Identify if it is true or false?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We are given with two Equation of circle let, x2 + y2 + 2g1x + 2g1x + c1 = 0 and x2 + y2 + 2g2x + 2g2x + c2 = 0
Let us consider the equation of the circle which cuts c1 and c2 orthogonally to be c.

We know that when a circle, c cuts the other Circle, c' orthogonally then it follows the Condition 2g ✕ g’ + 2f ✕ f’ = c + c’
Now, we first take circle c1 as c’ is cutting orthogonally.

…(1)
Now, let us Consider second circle c2, as c is cutting c2 orthogonally

…(2)
C = 0

Now we are putting the values of 'f ' and 'g' in the Equation of circle, C.
Question Image

On simplifying, we will get

The equation of a circle which cuts the other circle orthogonally.

Watch 3-min video & get full concept clarity