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Show that if the axes be turned through `7(1^(@))/(2)`, the equation `sqrt(3)x^(2)+(sqrt(3)-1)xy-y^(2)=0` become free of xy in its new form.

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ARIHANT MATHS-COORDINATE SYSTEM AND COORDINATES -Exercise For Session 4
  1. The equation of the locus of points equidistant from (-1-1) and (4,2...

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  2. The equation of the locus of a point which moves so that its distance ...

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  3. If the coordinates of a vartiable point P be (t+(1)/(t), t-(1)/(t)), w...

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  4. If the coordinates of a variable point be (cos theta + sin theta, sin ...

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  5. If a point moves such that twice its distance from the axis of x excee...

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  6. The equation 4xy-3x^(2)=a^(2) become when the axes are turned through ...

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  7. Transform the equation x^(2)-3xy+11x-12y+36=0 to parallel axes through...

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  8. Find the locus of a point equidistant from the point (2,4) and the ...

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  9. Find the equation of the locus of the points twice as from (-a, 0) as ...

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  10. OA and OB are two perpendicular straight lines. A straight line AB is ...

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  11. The ends of a rod of length l move on two mutually perpendicular lines...

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  12. The coordinates of three points O, A, B are (0, 0), (0,4) and (6, 0) r...

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  13. What does the equation (a-b)(x^2+y^2)-2a b x=0 become if the origin...

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  14. The equation x^(2)+2xy+4=0 is transformed to the parallel axes through...

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  15. Show that if the axes be turned through 7(1^(@))/(2), the equation sqr...

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  16. Find the angle through which the axes may be turned so that the equati...

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  17. Transform 12x^(2)+7xy-12y^(2)-17x-31y-7=0 to rectangular through the p...

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