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The coordinates of the vertices of a tri...

The coordinates of the vertices of a triangle are `[at_(1)t_(2),a(t_(1)+t_(2))],[at_(2),t_(3),a(t_(2)+t_(3))] and [at_(3)t_(1),t_(3)+t_(1))]`. Find the coordinates of the ortocentre of the triangle.

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The correct Answer is:
`[a-a(t_(1)+t_(2)+t_(3)+t_(1)+t_(2)t_(3)]`
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The vertices of a triangle are [at_1t_2, a(t_1+t_2)],[at_2t_3,a(t_2+t_3)],[at_3t_1,a(t_3+t_1)] Find the orthocentre of the triangle.

Find the area of the triangle with verrtices (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2))and(at_(3)^(2),2at_(3))

The vertices of a triangle are [a t_1t_2,a(t_1 +t_2)] , [a t_2t_3,a(t_2 +t_3)] , [a t_3t_1,a(t_3 +t_1)] Then the orthocenter of the triangle is (a) (-a, a(t_1+t_2+t_3)-at_1t_2t_3) (b) (-a, a(t_1+t_2+t_3)+at_1t_2t_3) (c) (a, a(t_1+t_2+t_3)+at_1t_2t_3) (d) (a, a(t_1+t_2+t_3)-at_1t_2t_3)

Let A(ct_(1), (c)/(t_(1))), B(ct_(2),(c)/(t_(2))) and C(ct_(3),(c)/(t_(3))) be the vertices of the triangle ABC. Show that the ortocentre of the triangle lies on xy=c^(2) .

If the Verticesof a triangle are P(at_1,a/t_1) , Q(at_2,a/t_2) and R(at_3,a/t_3) Show that the orthocentre of the triagle lies on xy = a^2 .

If the extremities of a focal chord of the parabola y^(2) = 4ax be (at_(1)^(2) , 2at_(1)) and (at_(2)^(2) ,2at_(2)) , show that t_(1)t_(2) = - 1

Establish gas equation, (P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2)) .

If the normal at (at_(1)^(2),2at_(1)) "to" y^(2)=4ax intesect the parabola at (at_(2)^(2),2at_(2)) "then" t_(1)+t_(2)+(k)/(t_(1))=0 (t_(1) ne 0) , find k.

Find the locus of the point (t^2-t+1,t^2+t+1),t in R .

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Prove analytically that the perpendicular bisector of the sides of a t...

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  2. The coordinates of the vertex A of the triangle ABC are (-5,2) the equ...

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  3. The coordinates of the vertices of a triangle are [at(1)t(2),a(t(1)+t(...

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  4. Prove that diagonals of the parallelogram formed by the four straight ...

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  5. Find the locus of the foot of the perpendicular from the origin upon ...

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  6. Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 alw...

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  7. Show that the locus of the point of intersection of the stright lines ...

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  8. Prove analytically that in any triangle the perpendiculars drawn from ...

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  9. Prove analytically that the bisectors of the interior angles of a tria...

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  10. If d(1),d(2),d(3) be the distances of a fixed point from the straight ...

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  11. Show that the quadrilateral formed by the four lines y=mx+a sqrt(a+m^(...

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  12. Show that the lines x cos alpha+ y alpha=p, x cos (alpha+ (2pi)/(3)) +...

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  13. 2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABC...

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  14. ABC is right-angle triangle, right -angled at A. The coordinates of B ...

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  15. The line through A( a cos theta,0) and perpendicular to the x-axis mee...

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  16. P and Q are two point on the line x-y+1=0, if O is the origin and bar...

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  17. O(0,0) and A(4,4) are two given points and B is any point. Find the eq...

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  18. Show that the image of the point (h,k) with respect to the striaight l...

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  19. A point moves so that sum of the squares of its distances from the ve...

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  20. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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