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Find the coordinates of the point at which the circles `x^2-y^2-4x-2y+4=0` and `x^2+y^2-12 x-8y+36=0` touch each other. Also, find equations of common tangents touching the circles the distinct points.

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Find the coordinates of the point at which the circles x^(2)-y^(2)-4x-2y+4=0 and x^(2)+y^(2)-12x-8y+36=0 touch each other.Also,find equations of common tangents touching the circles the distinct points.

find the coordinates of the points at which the circle x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-12x-8y=12 touch each other.Find 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.

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

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.

Show that the curvesy ^(2)=4x and x^(2)+y^(2)-6x+1=0 touch each other at (1,2). Also find the equation of the common tangent and normal.

Prove that the curve y^(2)=4x and x^(2)+y^(2)-6x+1=0 touches each other at thepoint (1,2), find the equation of the common tangents.

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 .

The two circles x^(2)+y^(2)-cx=0 and x^(2)+y^(2)=4 touch each other if:

A DAS GUPTA-Circles-EXERCISE
  1. AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = A...

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  2. Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it...

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  3. Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4...

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  4. A straight line AB is divided at C so that AC=3CB. Circles are describ...

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  5. If from any point P on the circle x^2+y^2+2gx+2fy+c=0 tangents are dra...

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  6. If the chord of contact of the tangents from a point on the circle x^2...

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  7. If the pole of a straight line with respect to the circle x^(2)+y^(2)=...

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  8. Tangents are drawn from the point (h,k) to ^circle x^2+y^2 =a^2; Prove...

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  9. Find the equation of the circle which has for its diameter the chord o...

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  10. If y=mx be the equation of a chord of the circle prove that the circle...

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  11. Prove that the circle x^2 + y^2-6x-4y+9=0 bisects the circumference of...

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  12. The equation of the circle on the common chord of the circles (x-a)^(2...

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  13. Find the equation of the circle passing through the intersection of th...

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  14. Find the equation of the circle passing through the point of intersect...

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  15. Find the equation of the circle whose diameter is the common chord of ...

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  16. The line Ax+By+=0 cuts the circle by x^2+y^2+Ax+By+C=0at P and Q. The ...

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  17. Prove that the equation x^(2)+y^(2)-2x-2ay-8=0, a in R represents the...

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  18. The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing ...

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  19. Consider a family of circles passing through two fixed points A (3,7) ...

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  20. If the circle C1: x^2 + y^2 = 16 intersects another circle C2 of radiu...

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