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Show that the line lx+my+n=0 is a normal...

Show that the line `lx+my+n=0` is a normal to the circles S=0 iff `gl+mf=mn`.

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The correct Answer is:
`hArr lg+ mf = n `
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Show that the line lx+my + n =0 is a normal to the circle S = 0 if and only if gl +mf = n

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AAKASH SERIES-CIRCLE-EXERCISE -1.4
  1. Show that the line lx+my+n=0 is a normal to the circles S=0 iff gl+mf=...

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  2. Discuss the relative position of the fol- lowing pair of circles. ...

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  3. Discuss the relative position of the fol- lowing pair of circles. ...

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  4. Find the number of possible common tangents that exist for the follo...

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  5. Find the number of possible common tangents that exist for the follo...

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  6. Find the number of possible common tangents that exist for the follo...

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  7. Show that the circles x^(2) +y^(2) -4x-6y-12=0 and 5(x^(2)+y^(2))-...

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  8. Show that x^(2) + y^(2) -6x -9y +13 =0, x^(2) +y^(2) -2x -16y =0 touch...

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  9. Show that the circles x^(2) + y^(2)-4x-6y-12=0 and x^(2) +y^(2) +...

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  10. Find the equation of the circle which touches the circle x^(2) + y^(...

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  11. Show that the circles S=-x^(2) + y^(2) -2x-4y -20 =0 , S' = x^(2) +y^...

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  12. Show that the four common tangents can be drawn for the circles give...

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  13. Prove that the circles x^(2) + y^(2) -8x -6y +21=0 and x^(2) + y^(2) ...

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  14. Find the direct common tangents of the circles x^(2) + y^(2) +22x -4y...

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  15. Find the transberes common tangents of the circles x^(2) + y^(2) -4...

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  16. Find all common tangents of the pairs of circles x^(2) +y^(2) =0 a...

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  17. Find all common tangents of the pairs of circles x^(2) +y^(2) +4x ...

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  18. Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0. Suppose that...

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  19. Find the value of c for which A(2,0),B(0,14//3) ,C(4,5) and D(0,c) a...

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  20. The area of the quadrilateral formed by the tangents from the point (4...

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  21. Discuss the relative position of the fol- lowing pair of circles. ...

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