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Find the equation of the circle whose centre is at `(3,-1)` and which cuts off a chord of length `6u n i t s` on the line `2x-5y+18=0.`

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To find the equation of the circle with center at (3, -1) that cuts off a chord of length 6 units on the line given by the equation \(2x - 5y + 18 = 0\), we can follow these steps: ### Step 1: Write the general equation of the circle The general equation of a circle with center \((h, k)\) and radius \(r\) is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \] Here, the center is \((3, -1)\), so we can write: ...
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RD SHARMA-THE CIRCLE-Solved Examples And Exercises
  1. Find the equation of the circle which touches the x-axis and passes t...

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  2. Find the equation of the circle which passes through the origin and ...

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  3. Find the equation of the circle whose centre is at (3,-1) and which...

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  4. A rectangle A B C D is inscribed in a circle with a diameter lying ...

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  5. Find the equation of a circle with origin as centre and which circu...

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  6. Find the equation of a circle whose diameters are 2x-3y+12a n dx+4y-5=...

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  7. Find the equation of a circle of radius 5 whose centre lies on x-axis ...

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  8. If y=2x is a chord of the circle x^2+y^2-10 x=0 , find the equation of...

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  9. Find the equation of the circle is (2,-3) and radius is 8.

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  10. Find the equation of the circle which passes through the point of i...

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  11. Find the equation of the circle having centre at (3,-4) and touching t...

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  12. Find the circle and radius of the circle given by the equation 2x^2...

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  13. If the line 2x-y+1=0 touches the circle at the point (2,5) and the cen...

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  14. Find the equation of the circle concentric with the circle 2x^2+2y^...

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  15. Find the equation of a circle whose centre is (2,-3) and radius 5.

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  16. If the equations of the two diameters of a circle are x-y=5\ and \ 2x+...

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  17. Find the equation of the circle which passes through two points on the...

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  18. A circle of radius 6 units touches the coordinates axes in the first ...

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  19. Show that the equation of the circle which touches the coordinates axe...

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  20. Find the equation of the circle which touches the coordinate axes and ...

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