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Prove that the circle x^(2) + y^(2) + 2a...

Prove that the circle `x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0` touch each other if
`(1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2))` .

Text Solution

Verified by Experts

The correct Answer is:
`c^(2)(a^(2)+b^(2))=a^(2)b^(2)or(1)/(a^(2))+(1)/(b^(2))=(1)/(c^(2))`
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ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
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  5. Find the derivative of (4x - 2)

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  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  8. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  9. If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of ...

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  10. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  11. Find the derivative of (ax + b)^n

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  12. Consider a family of circles which are passing through the point (-1,1...

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  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  15. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  16. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

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  17. The point diametrically opposite to the point P(1, 0) on the circle x^...

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