If the circles x ^(2) +y^(2) +2gx +2fy =...

If the circles `x ^(2) +y^(2) +2gx +2fy =0 and x ^(2) +y^(2) +2g'x+ 2f'y=0` touch each other then-

A

`f f' =g g'`

B

`fg=f'g'`

C

`f^(2)g =f' g'`

D

`f g' =gf'`

Text Solution

Verified by Experts

The correct Answer is:

D

Topper's Solved these Questions

MCQ's
CHHAYA PUBLICATION|Exercise QUESTION PAPER 6|90 Videos
MCQ ZONE 3
CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos
Measures of Central Tendency
CHHAYA PUBLICATION|Exercise Exercise 2 C Very short answer type question|18 Videos

Similar Questions

Explore conceptually related problems

Show that the two circles x^(2) + y^(2) + 2gx + 2fy = 0 and x^(2) + y^(2) + 2g'x+ 2f'y = 0 will touch each other if f'g = g'f.

If two cricles x^2 + y^2 + 2gx + 2fy = 0 and x^2 +y^2 + 2g'x + 2f'y = 0 touch each other, then

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

Show that the circles x^(2) + y^(2) - 8x - 4y - 16 = 0 and x^(2) + y^(2) - 2x + 4y + 4 = 0 touch each other internally and find the coordinates of their point of contact.

Show that the circles x^(2) + y^(2) + 6x + 14y + 9 = 0 and x^(2) + y^(2) - 4x - 10y - 7 = 0 touch each other externally, find also the equation of the common tangent of the two circles.

Show that the circles x^(2) + y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch each other externally, find the coordinates of their point of contact.

Prove that the circles x^(2) + y^(2) - 2x - 4y - 12 = 0 and 3x^(2) + 3y^(2) - 2x + 4y - 140 = 0 touch each other. Find the coordinates of the point of contact.

Prove that the circles x^(2) + y^(2) + 4x - 10y - 20 = 0 and x^(2) + y^(2) - 4x - 4y + 4 = 0 touch each other internally. Find the equation of their common tangent.

If the circle x ^(2) +y^(2) -4rx- 2ry+4r^(2)=0 and x^(2) +y^(2) =25 touch each other, then r satisfies-

Show that the circles x^(2) + y^(2) + 6x + 2y + 8 = 0 and x^(2) + y^(2) + 2x + 6y + 1 = 0 intersect each other.

CHHAYA PUBLICATION-MCQ's-QUESTION PAPER 9

The coordinate of the vertices B and C of the triangle ABC are (5,2,8)...
Text Solution
|
If P is a point such that the ratio of the squares of rthe lengths of ...
Text Solution
|
If the circles x ^(2) +y^(2) +2gx +2fy =0 and x ^(2) +y^(2) +2g'x+ 2f'...
Text Solution
|
The equation of the line bisecting perpendicularly the segmwent joinin...
Text Solution
|
The ratio in which the line-segment joining the points (2,-3, -5) and(...
Text Solution
|
A square of side a lies above the x-axis and has one vertex at the ori...
Text Solution
|
The triangle formed by the lines x+y =0,3x+y=4 and x+3y=4 is-
Text Solution
|
The base vertices of an isosceles triangle PQR are Q (1,3) and R(-2, 7...
Text Solution
|
The distance of the line 2x -3y =4 from the point (1,1) measured paral...
Text Solution
|
The equation of the circle with origin as centre and passing through t...
Text Solution
|
A point moves such that the area of the triangle formed by it with the...
Text Solution
|
The length of the tangent drawn from any point on the circle x ^(2) +y...
Text Solution
|
A point moves on a plane such that its distance from the point (3,0) ...
Text Solution
|
If the major and minor axes of the ellipse are the axes of coordinates...
Text Solution
|
Let m be the slope of a system of parallel chords of the parabola y ^(...
Text Solution
|
The locus of the mid-point of the line segment joining the focus to a...
Text Solution
|
Let R be the relation on the set A of first eight natural numbers defi...
Text Solution
|
Out of 40 boys 30 can swim, 27 can play chess and only 5 can fo neithe...
Text Solution
|
For two sets A and B , the three elements of AxxB are (a,x), (b,y) , ...
Text Solution
|
The coordinates of the foci of a hyperbola are (0,4) and (0,-4) and th...
Text Solution
|