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If `(x , y)` and `(x ,y)` are the coordinates of the same point referred to two sets of rectangular axes with the same origin and it `u x+v y ,` where `u` and `v` are independent of `xa n dy` , becomes `V X+U Y ,` show that `u^2+v^2=U^2+V^2dot`

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. For points P-=(x1, y1) and Q-=(x2, y2) of the coordinate plane, a new ...

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  2. Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5...

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  3. If (x , y) and (x ,y) are the coordinates of the same point referred t...

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  4. O X and O Y are two coordinate axes. On O Y a fixed point P(0,c) is t...

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  5. Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of...

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  6. The vertices of a triangle are [a t1t2,a(t1 +t2)], [a t2t3,a(t2 +t3)],...

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  7. If (-6,-4),(3,5),(-2,1) are the vertices of a parallelogram, then the...

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  8. The maximum area of the triangle whose sides a,b and c satisfy 0leqale...

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  9. If (-4,0) and (1,-1) are two vertices of a triangle of area 4s qdotu n...

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  10. Let O-=(0,0),A-=(0,4),B-=(6,0)dot Let P be a moving point such that th...

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  11. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

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  12. The vertices A and D of square A B C D lie on the positive sides of x ...

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  13. A light ray emerging from the point source placed at P(2,3) is reflect...

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  14. If the origin is shifted to the point ((a b)/(a-b),0) without rotation...

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  15. In A B C , the coordinates of B are (0,0),A B=2,/A B C=pi/3, and t...

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  16. If a triangle A B C ,A-=(1,10), circumcenter -=(-1/3,2/3), and orthoce...

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  17. A triangle ABC with vertices A(-1,0),B(-2,3/4) & C(-3,-7/6) has its or...

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  18. In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0)...

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  19. If the vertices of a triangle are (sqrt(5,)0) , (sqrt(3),sqrt(2)) , an...

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  20. The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), a...

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