Home
Class 12
MATHS
If the circles x^2+y^2+2a x+c=0a n dx^2+...

If the circles `x^2+y^2+2a x+c=0a n dx^2+y^2+2b y+c=0` touch each other, then `(a) 1/(a^2)+1/(b^2)=1/c` (b) `1/(a^2)+1/(b^2)=1/(c^2)` (c) `a+b=2c` (d) `1/a+1/b=2/c`

A

`1//c`

B

c

C

`(1)/(c^(2))`

D

`c^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`x^(2)+y^(2)+2ax+c=0,x^(2)+y^(2)+2by+c=0`
Common tangent at common point `ax-by=0`
Perpendicular distance from centre = radius
`x^(2)+y^(2)+2ax+c=0" "(-a,0)`
`|(-a^(2))/(sqrt(a^(2)+b^(2)))|=sqrt(a^(2)-c)impliesa^(4)=(a^(2)+b^(2))(a^(2)-c)`
`a^(4)=a^(4)+a^(2)b^(2)-c(a^(2)+b^(2))`
`(1)/( c )=(1)/(a^(2))+(1)/(b^(2))`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN - 5

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|5 Videos

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|10 Videos

  • JEE MAIN REVISION TEST - 30 | JEE -2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

If the circles x^(2)+y^(2)+2ax+c=0andx^(2)+y^(2)+2by+c=0 touch each other then show that (1)/(a^(2)),(1)/(2c),(1)/(b^(2)) are in A.P.

Prove that the circle x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other if (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

If two circles x^(2)+y^(2)+c^(2)=2ax and x^(2)+y^(2)+c^(2)-2by=0 touch each other externally , then prove that (1)/(a^(2))+(1)/(b^(2))=(1)/(c^(2))

If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) touch each other, then

If the circles x^2+y^2=a\ a n d\ x^2+y^2-6x-8y+9=0 touch externally then a= a. 1 b. -1 c. 21 d. 16

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a ,b ,c and a^prime ,b^(prime),c ' from the origin, then a. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0 b. 1/(a^2)-1/(b^2)-1/(c^2)+1/(a^('2))-1/(b^('2))-1/(c^('2))=0 c. 1/(a^2)+1/(b^2)+1/(c^2)-1/(a^('2))-1/(b^('2))-1/(c^('2))=0 d. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then (a) a+b+c=0 (b) a+b=2 (c) b-c=1 (d) a+c=-2

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then a+b+c=0 a+b=2 b-c=1 (d) a+c=-2

If x=asecthetacosvarphi , y=bsecthetasinvarphi and z=ctantheta , then (x^2)/(a^2)+(y^2)/(b^2)= (a) (z^2)/(c^2) (b) 1-(z^2)/(c^2) (c) (z^2)/(c^2)-1 (d) 1+(z^2)/(c^2)