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Prove that the line ax + by + c = 0 will...

Prove that the line ax + by + c = 0 will be a tangent to the circle `x^2+y^2=r^2` if `r^2(a^2+b^2)=c^2`.

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MBD PUBLICATION-CONIC SECTIONS-QUESTION BANK
  1. Find the equation of the tangents to the circle x^2+y^2-2x+4y=4, paral...

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  2. Show that the line x - 7y + 5 = 0 is a tangent to the circle x^2+y^2-5...

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  3. Prove that the line ax + by + c = 0 will be a tangent to the circle x^...

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  4. prove that the line 2x + y = 1 is a tangent to the circle x^2+y^2+6x-4...

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  5. If the line 4y - 3x = k is a tangent to the circle x^2+y^2+10x-6y+9=0 ...

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  6. Find the length of the tangent, drawn to the circles x^2+y^2+10x-6y+8=...

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  7. Find the length of the tangent drawn from the point (2, -1) to the cir...

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  8. Find the length of the tangent drawn from the point (4, 7) to the circ...

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  9. Prove that the circles given by the equations x^2+y^2+2x-8y+8=0 and x^...

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  10. Prove that the circles given by the equations x^2+y^2=4 and x^2+y^2+6x...

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  11. Prove that the two circles x^2+y^2+2by+c^2=0 and x^2+y^2+2ax+c^2=0, wi...

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  12. Prove that the circles given by x^2+y^2+2ax+2by+c=0, and x^2+y^2+2bx+2...

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  13. Find the equation of the circle through the point of intersection of c...

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

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  15. Find the radical axis of the circles x^2+y^2-6x-8y-3=0 and 2x^2+2y^2+4...

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  16. Find the radical axis of the circles x^2+y^2-6x+8y-12=0 and x^2+y^2+6x...

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  17. If centre of one circle lies on or inside another, prove that the circ...

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  18. If a circle S intersects circles S1 and S2 orthogonally. Prove that th...

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  19. R is the radical centre of circles S1, S2 and S3. Prove that if R is o...

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  20. Determine a circle which cuts orthogonally each of the circles. S1 : x...

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