Home
Class 12
MATHS
Prove that the circles x^2+y^2+24ux+2vy=...

Prove that the circles `x^2+y^2+24ux+2vy=0` and `x^2+y^2+2u_1x+2v_1y=0` touch each other externally if `-12u_1u=v_1v`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    FIITJEE|Exercise Assignment Problems (Subjective ) Level -I|16 Videos

  • CIRCLE

    FIITJEE|Exercise Assignment Problems (Subjective ) Level -II|13 Videos

  • CIRCLE

    FIITJEE|Exercise Exercise 3|6 Videos

  • AREA

    FIITJEE|Exercise Numerical Based|3 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each other

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

Prove that the circles x^(2)+y^(2)+2ax+2ax+2by=0 and x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 touch each other if, ab_(1),a_(1)b .

The circles x^2 + y^2 + 2ux + 2vy = 0 and x^2 + y^2 + 2u_1 x + 2v_1 y = 0 touch each other at (1, 1) if : (A) u + u_1 = v + v_1 (B) u + v = v_1 + u_1 (C) u/u_1 = v/v_1 (D) none of these

Show that the circles x ^(2) + y ^(2) - 2x =0 and x ^(2) + y ^(2) - 8x + 12=0 touch each other externally. Find the point of contact.

Examine whether the two circles x^2+y^2-2x-4y=0 and x^2+y^2-8y-4=0 touch each other externally or internally .

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

If circles x^(2) + y^(2) = 9 " and " x^(2) + y^(2) + 2ax + 2y + 1 = 0 touch each other , then a =