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What does the equation 2x^2+4x y-5y^2+20...

What does the equation `2x^2+4x y-5y^2+20 x-22 y-14=0` become when referred to the rectangular axes through the point `(-2,-3)` , the new axes being inclined at an angle at `45^0` with the old axes?

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The equation of a curve referred to a given system of axes is 3x^2+...

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  2. Determine x so that the line passing through (3,4) and (x ,5) makes ...

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  3. What does the equation 2x^2+4x y-5y^2+20 x-22 y-14=0 become when re...

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  4. Shift the origin to a suitable point so that the equation y^2+4y+8x...

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  5. At what point should the origin be shifted if the coordinates of a ...

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  6. Find the equation to which the equation x^2+7x y-2y^2+17 x-26 y-60=0...

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  7. The equation of curve referred to the new axes, axes retaining thei...

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  8. If the point (2,3),(1,1), and (x ,3x) are collinear, then find the val...

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  9. Which line is having the greatest inclination with the positive dire...

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  10. Find the orthocentre of Delta A B C with vertices A(1,0),B(-2,1), ...

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  11. The angle between the line joining the points (1,-2) , (3,2) and the l...

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  12. The line joining the points A(2,1) and B(3,2) is perpendicular to the...

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  13. For what value of k are the points (k ,2-2k)(-k+1,2k)a n d(-4-k ,6,6-2...

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  14. Find the area of the quadrilateral A B C D having vertices A(1,1),B(...

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  15. Given that P(3,1),Q(6. 5), and R(x , y) are three points such that t...

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  16. If O is the origin and if the coordinates of any two points Q1 \ a n...

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  17. Prove that the area of the triangle whose vertices are (t ,t-2),(t+...

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  18. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

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  19. In A B C Prove that A B^2+A C^2=2(A O^2+B O^2) , where O is the ...

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  20. Two points O(0,0) and A(3,sqrt(3)) with another point P form an ...

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