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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.

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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 .

NAGEEN PRAKASHAN-CONIC SECTION-Exercise 11A
  1. Find the diameter of the circle 2x^(2)+2y^(2)-6x-9=0.

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  2. Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-4y-11...

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  3. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

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  4. Prove that the circles x^(2)+y^(2)+2ax+ay-3a^(2)=0andx^(2)+y^(2)-8ax-6...

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  5. If the circles x^(2)+y^(2)+2ax+c=0andx^(2)+y^(2)+aby+c=0 touch each o...

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  6. (i) Find the point at which the circle x^(2)+y^(2)-5x+2y+6=0, meets th...

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  7. (i) Find the equation of a circle concentric with the circle x^(2)+y^(...

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  8. Find the distance between the centres of the circles x^(2)-y^(2)+8x+10...

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  9. Find the equations of the circles the end points of whose diameter are...

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  10. The end points of a diameter of a circle are (1,-1) and (3,5). Find th...

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  11. Find the equation of a circle passes through the origin and cuts 'a' i...

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  12. (i) Find the equation of a circle passes through the origin and cuts t...

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  13. Show that equations of a circle with end points of diameter (x(1),y(1)...

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  14. Find the equation of a circle whose centre is (2,-1) and touches the l...

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  15. Find the equation of a circle with centre (1,-3) and touches the line ...

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  16. Find the equation of circle passing through the point (2,1), (1,2) and...

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  17. Find the equation of the circle which passes through the points (3,-2)...

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  18. Find the equation of the circle passing through the points (1,-2)a ...

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  19. Find the equation of circle passing through the points (0,5) and (6,1)...

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  20. Find the equation of circle passing through the points (1,-2) and (3,-...

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