Show that the circles x^2+y^2-10 x+4y-20...

Show that the circles `x^2+y^2-10 x+4y-20=0` and `x^2+y^2+14 x-6y+22=0` touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

touch externally

intersect in real points

do not intersect

one is contained in the other

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

THE CIRCLE
ML KHANNA|Exercise Problem Set (4) (TRUE AND FALSE) |4 Videos
THE CIRCLE
ML KHANNA|Exercise Problem Set (4) (FILL IN THE BLANKS) |1 Videos
THE CIRCLE
ML KHANNA|Exercise Problem Set (3) (FILL IN THE BLANKS) |11 Videos
TANGENTS AND NORMALS
ML KHANNA|Exercise SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)|19 Videos
THE ELLIPSE
ML KHANNA|Exercise SELF ASSESSMENT TEST|9 Videos

Similar Questions

Explore conceptually related problems

Show that the circles x^(2)+y^(2)-10x+4y-20=0 and x^(2)+y^(2)+14x-6y+22=0 touch each other.Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Find the coordinates of the points at which the circles x^2+y^2-4x-2y=4 and x^2+y^2-12x-8y=12 touch each other. Find the coordinates of the point of contact and equation of the common tangent at the point of contact.

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.

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

If the circles x^2+y^2+2x-8y+8=0 and x^2+y^2+10x-2y+22=0 touch each other find their point of contact

Show that the two circles x^(2) + y^(2) - 4x + 10y + 20 = 0 and x^(2) + y^(2) + 8x - 6y - 24 =0 touch each other . Also , find co-ordinates of their point of contact .

Show that the two circles x^(2) + y^(2) + 4x - 12 y + 4 = 0 and x^(2) + y^(2) - 2x - 4y + 4 = 0 touch each other . Also , find the co-ordinates of the point of contact .

ML KHANNA-THE CIRCLE -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)

The circles x^(2)+ y^(2) -6x-2y +9 = 0 and x^(2) + y^(2) =18 are such...
Text Solution
|
If the two circles a(x^(2)+y^(2))+bx+cy=0 and p(x^(2)+y^(2))+qx+ry=0...
Text Solution
|
Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...
Text Solution
|
The two circles x^(2)+y^(2)-5=0 and x^(2)+y^(2)-2x-4y-15=0
Text Solution
|
Consider the circles x^2+(y-1)^2=9,(x-1)^2+y^2=25. They are such that ...
Text Solution
|
Two circles x^(2) + y^(2) - 2x - 4y = 0 and x^(2) + y^(2) - 8y...
Text Solution
|
The circle S(1)(a(1),b(1)), r(1) touches externally the circles S(2) ...
Text Solution
|
The circles x^(2)+y^(2)-4x+6y+8=0 and x^(2)+y^(2)-10x-6y+14=0
Text Solution
|
Equation of a circle with centre (4,3) touching the circle x^(2)+y^(2)...
Text Solution
|
Centre of the circle whose radius is 3 and which touches internally th...
Text Solution
|
Equation of the circle touching the circle x^(2) + y^(2) -15x + 5y =0 ...
Text Solution
|
If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2)...
Text Solution
|
The locus of centre of the circle which touches the circle x^(2)+(y-1)...
Text Solution
|
The circle x^(2)+y^(2)-2ax+c^(2)=0 and x^(2)+y^(2)-2by+c^(2)=0 will ...
Text Solution
|
The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each...
Text Solution
|
Given the equation of two circles x^(2)+y^(2)=r^(2) and x^(2) +y^(2) ...
Text Solution
|
If the two circles x^(2) + y^(2) =4 and x^(2) +y^(2) - 24x - 10y +a^(2...
Text Solution
|
If two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 int...
Text Solution
|
The number of common tangents to the circles x^(2)+y^(2)+2x+8y-23=0...
Text Solution
|
The number of common tangents to the circles x^(2)+y^(2) -x=0, x^(2)+...
Text Solution
|