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Let A = (-2,0) and B = (1,0) and P is a ...

Let `A = (-2,0) and B = (1,0) and P` is a variable point such that `/_APB = 60^@.` Prove analytically that the locus of P is a circle. Find its radius and centre.

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A DAS GUPTA-Circles-EXERCISE
  1. The equation of three circles are given x^2+y^2=1,x^2+y^2-8x+15=0,x^2+...

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  2. From a point P, tangents drawn to the circle x^2 + y^2 + x-3=0, 3x^2 +...

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  3. Let A = (-2,0) and B = (1,0) and P is a variable point such that /APB ...

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  4. A point moves such that the sum of the squares of its distances from t...

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  5. Two rods of lengths aa n db slide along the x- and y-a xi s , respecti...

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  6. A variable circle passes through the point P (1, 2) and touches the x-...

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  7. From the point A (0, 3) on the circle x^2+4x+(y-3)^2=0 a chord AB is d...

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  8. From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1. The...

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  9. A circle of radius 'r' passes through the origin O and cuts the axes a...

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  10. A circle of radius r passes through the origin O and cuts the axes at ...

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  11. Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2...

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  12. Let A be one point of intersection of two intersecting circles with ce...

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  13. Prove that the locus of a point which moves such that the sum of th...

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  14. The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes i...

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  15. A triangle has two of its sides along the axes, its third side touches...

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  16. The locus of the perpendiculars drawn from the point (a, 0) on tange...

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  17. Let S-=x^2+y^2+2gx+2f y+c= be a given circle. Find the locus of the fo...

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  18. Show that the locus of points from which the tangents drawn to a circl...

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  19. Find the locus of the point of intersection of tangents to the circle ...

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  20. The circle x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two ...

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