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Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=...

Prove that `x^2+y^2=a^2` and `(x-2a)^2+y^2=a^2` are two equal circles touching each other.

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Prove that the circle x^2 + y^2 =a^2 and (x-2a)^2 + y^2 = a^2 are equal and touch each other. Also find the equation of a circle (or circles) of equal radius touching both the circles.

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A DAS GUPTA-Circles-EXERCISE
  1. 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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  2. Two circles, each of radius 5 units, touch each other at (1, 2). If th...

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  3. Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touc...

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  4. The equation of the circle which touches the circle x^2+y^2-6x+6y+17 =...

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  5. Find the area of equilateral triangle inscribed in a circle x^2+y^2+2g...

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  6. Find the area of the triangle formed by the tangents from the point (4...

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  7. Find the equations of the circles passing through the point (-4,3) and...

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  8. The equation of one of the circles which touch the pair of lines x^2 -...

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  9. Lines 5x + 12 y -10=0 and 5x - 12y - 40=0touch a circle C(1) of diamet...

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  10. Find the equation of the circle passing through the points A(4,3). B(...

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  11. A circle touches both the x-axis and the line 4x-3y+4=0. Its centre is...

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  12. Obtain the equations of the straight lines passing through the point A...

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  13. The extremities of a diagonal of a rectangle are (-4,4) and (6,-1). A...

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  14. Tangents are drawn to the circle x^(2) + y^(2) = 12 at the points wher...

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  15. Find the equation of the tangent to the circle x^2 + y^2 - 80x - 60y +...

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  16. The tangent to the circle x^(2)+y^(2)=5 at the point (1, -2) also touc...

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  17. AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = A...

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

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

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

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