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Let A = (0,1) and B=(-p/2,(q+1)/2) be tw...

Let `A = (0,1) and B=(-p/2,(q+1)/2)` be two fixed points in a plane. Let C denote a circle with centre B and passing through A. Prove that the real roots of the equation `x^2 + px + q = 0` are given by the abscissae of the points of intersection of C with the x-axis.

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A DAS GUPTA-Circles-EXERCISE
  1. Find the equation of the circle which passes through the points (1,-2)...

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  2. The abscissa of the two points A and B are the roots of the equation x...

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  3. Let A = (0,1) and B=(-p/2,(q+1)/2) be two fixed points in a plane. Let...

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  4. Find the area of the triangle formed by the lines y = x, y= 2x, y=3x+4

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  5. Find the length of the chord x^2+y^2-4y=0 along the line x+y=1. Also f...

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  6. Prove that the circles x^2 + y^2-9 = 4r^2,r = 1,2,3 cut off equal int...

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  7. Determine all those values of p in R for which two chords can be drawn...

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  8. A circle of radius 2 lies in the first quadrant and touches both the a...

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  9. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

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  10. Two circles, each of radius 5 units, touch each other at (1, 2). If th...

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  11. Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touc...

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  12. The equation of the circle which touches the circle x^2+y^2-6x+6y+17 =...

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  13. Find the area of equilateral triangle inscribed in a circle x^2+y^2+2g...

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  14. Find the area of the triangle formed by the tangents from the point (4...

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  15. Find the equations of the circles passing through the point (-4,3) and...

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  16. The equation of one of the circles which touch the pair of lines x^2 -...

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  17. Lines 5x + 12 y -10=0 and 5x - 12y - 40=0touch a circle C(1) of diamet...

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  18. Find the equation of the circle passing through the points A(4,3). B(...

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  19. A circle touches both the x-axis and the line 4x-3y+4=0. Its centre is...

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  20. Obtain the equations of the straight lines passing through the point A...

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