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The corodinates of the three vertices of...

The corodinates of the three vertices of a triangle are `(a, a tan alpha) , (b ,b tan beta) and (c, c tangamma)`. If the circumcentre and orthocentre of the triangle are at (0,0) and (h,k) respectively, prove that `(h)/(k)=(cos alpha+ cos beta+ cos gamma)/( sin alpha+ sin beta + sin gamma)`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
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  2. A chord AB of the circle x^(2)+y^(2)=a^(2) subtends a right angle at i...

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  3. The corodinates of the three vertices of a triangle are (a, a tan alph...

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  4. The triangle PQR is inscribed in the circle x^(2)+y^(2)=25. If Q and ...

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  5. Let L(1) be a striaght line passing through the origin and L(2) be the...

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  6. A rectangle PQRS has its side PQ paralle to the line y=mx and vertices...

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  7. If two distinct chords, drawn from the point (p,q) on the circle x^(2)...

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  8. A variable line L passing through the point B(2,5) intesects the lines...

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  9. For all values of a and, b show that the circle (x-2)(x-2+a)+(y+3) (y+...

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  10. A circle C(1) of diameter 6 units, is in the first quadrant and it tou...

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  11. Find he point on the straight line y=2x+11 which is nearest to the cir...

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  12. On the parabola y^(2)=4ax, P is the point with parameter t,Q is the op...

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  13. Through the vertex A of a parabola the chords AP and AQ are drawn at ...

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  14. Show that the sum of the ordinate of end of any chord of a system of p...

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  15. An equilateral triangle is inscribed within the parabola y^(2)=4ax wit...

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  16. P,Q and R three points on the parabola y^(2)=4ax. If Pq passes through...

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  17. A line of length (a+b) unit moves in such a way that its ends are alwa...

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  18. show that the length of the focal chord of the ellipse (x^(2))/(a^(2))...

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  19. A rod of given length (a+b) unit moves so that its ends are always on ...

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  20. If theta and phi be the eccentric angles of the extremities of a focal...

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