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Show that for all values of p, the circl...

Show that for all values of p, the circle `x^(2) + y^(2) - x(3p+4) - y(p-2) + 10p = 0` passes through the point (3, 1). If p varies, find the locus of the centre of the above circle.

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The correct Answer is:
x - 3y = 5
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CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Short Answer Type Questions)
  1. A circle touches y-axis at (0, 5) and whose centre lies on the line 2x...

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  2. Find the equation of a circle which passes through the point (4, 2) an...

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  3. Two cirles of radii 2 and 10 units respectively pass through (2, 4) an...

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  4. Prove that the point (-1, -2) lies on the circle x^(2) + y^(2) - x y -...

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  5. Show that for all values of p, the circle x^(2) + y^(2) - x(3p+4) - y(...

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  6. Find the coordinates of points equidistant from the axes and lying on ...

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  7. Find the equation to the common chord of the two circles x^(2) + y^(2)...

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  8. Find the equation of the common chord of the two circles x^(2)+y^(2)-4...

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  9. Find the equation of the circles which passes through the origin and t...

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  10. A point moves in such a manner that the sum of the squares of its dist...

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  11. A(3, 0) and B(-3, 0) are two given points and P is a moving point : if...

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  12. Show that the locus of the point of intersection of the lines x cos al...

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  13. Whatever be the values of theta, prove that the locus of the point of ...

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  14. Show that, x = (1)/(2)(3+5 cos theta), y = (1)/(2)(-4 + 5 sin theta) r...

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  15. Prove that the square of the distance between the two points (x(1), y(...

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  16. The equations of two diameters of a circle are x-2y+1 = 0 and x+y -2 =...

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  17. Find the equation of the circle circumscribing the rectangle whose sid...

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  18. A and B are two fixed points on a plane and P moves on the plane in su...

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  19. Show that the equation of the circle described on the chord x cos alph...

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  20. Find the circumcentre and circumradius of the triangle formed by the l...

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