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The points A(0,0),B(cosalpha,sinalpha) a...

The points `A(0,0),B(cosalpha,sinalpha)` and `C(cosbeta,sinbeta)` are the vertices of a right-angled triangle then

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The points A(0, 0), B(cos alpha, sin alpha) and C(cos beta, sin beta) are the vertices of a right angled triangle if :

Prove that the points A(1, -3), B (-3, 0) and C(4, 1) are the vertices of an isosceles right- angled triangle. Find the area of the triangle.

Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If all the vertices of a triangle have integral coordinates, then th...

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  2. The locus of a point represent by x=(a)/(2)((t+1)/(t)),y=(a)/(2)((t-...

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  3. The points A(0,0),B(cosalpha,sinalpha) and C(cosbeta,sinbeta) are the ...

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  4. The ends of a diagonal of a square are (2,-3) and (-1,1)dot Another ve...

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  5. Point P(p ,0),Q(q ,0),R(0, p),S(0,q) form (a) parallelogram (b) rhombu...

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  6. A rectangular billiard table has vertices at P(0,0),Q(0,7),R(10 ,7), ...

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  7. If one side of a rhombus has endpoints (4, 5) and (1, 1), then the ...

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  8. A rectangle A B C D , where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) , under...

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  9. If a straight line through the origin bisects the line passing through...

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  10. Let Ar ,r=1,2,3, , be the points on the number line such that O A1,O...

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  11. The vertices of a parallelogram A B C D are A(3,1),B(13 ,6),C(13 ,21),...

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  12. Point A and B are in the first quadrant; point O is the origin. If the...

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  13. In a A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3), point A lies on the li...

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  14. If y=ae^(mx)+be^(-mx), then (d^2y)/dx^2-m^2y is equals to (a)....

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  15. The vertices of a triangle are A(-1,-7),B(5,1)a n dC(1,4)dot If the ...

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  16. The points (0,8/3),(1,3) and (82 ,30) are the vertices of (A) an obtu...

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  17. Consider the triangle whose vertices are (0,0),(5,12) and (16 ,12) Fi...

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  18. A Point A divides the join of P(-5,1) and Q(3.5) in the ratio k:1. The...

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  19. Find the equation of the circle having center at (2,3) and which tou...

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  20. If the lines x+y=6 and x+2y=4 are diameters of the circle which passes...

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