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The vertices of a triangle are : P(x1,x1...

The vertices of a triangle are : `P(x_1,x_1 tan theta_1),Q (x_2, x_2tantheta_2)` and `R(x_3, x_3tantheta_3)`. If the circumcentre of `trianglePQR` coincides with the origin and `H(bar x,bar y)` is the orthocentre, show that : `bar y/bar x= (sintheta_1+sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3)` .

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
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  2. Find the centroid, incentre, circumcentre and orthocentre of the trian...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the area of the equilateral triangle that can be inscribed in the...

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  19. Find the equation of the circle circumscribing the quadrilateral forme...

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  20. If lines 5x + 12y-10 = 0 and 5x- 12y - 40 =0 touch a circle C1 of diam...

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