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Show that the perpendicular drawn from the point (4, 1) on the line segment joining (6, 5) and (2,-1) divides it internally in the ratio 8 : 5.

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Find the equation of the perpendicular drawn from the point (2,4,-1) to the line (x+5)/1=(y+3)/4=(z-6)/-9

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In what ratio does the point (- 4, 6) divide the line segment joining the points A(- 6, 10) and B(3,- 8)?

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Let the opposite angular points of a square be (3, 4) and (1, -1). Fin...

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  2. Using the concept of slope, prove that medians of an equilateral trian...

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  3. Show that the perpendicular drawn from the point (4, 1) on the line se...

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  4. A rectangle has opposite vertices at the points (1,2) and (5, 5). If t...

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  5. Find the centroid, incentre, circumcentre and orthocentre of the trian...

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  6. The vertices of a triangle are : P(x1,x1 tan theta1),Q (x2, x2tantheta...

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  7. The points (1, 3) and (5, 1) are the opposite vertices of a rectangle....

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  8. One side of a rectangle lies along the line 4x + 7y +5=0. Two of its v...

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  9. The consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y =...

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  10. One side of a square is inclined to the x-axis at an angle alpha and o...

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  11. On the portion of the line x + 3y - 3 = 0, which is intercepted betwee...

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  12. Find the direction in which a straight line must be drawn through the ...

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  13. The hypotenuse of a right triangle has its ends at the points (1, 3) a...

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  14. A ray of light passes through the point (1, 2) reflects on the x-axis ...

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  15. A person standing at the junction (crossing) of two straight paths rep...

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  16. Let (2, 1), (- 3, -2) and (a, b) form a triangle. Show that the collec...

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  17. Does the point (-2.5, 3.5) lie inside, outside or on the circle x^2 + ...

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  18. Prove that the centres of the three circles : x^2 + y^2 -4x-6y-14=0, x...

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  19. Prove that, through three given points which are not collinear, there ...

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  20. Find equations to the circles touching Y-axis at (0,3) and making inte...

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