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Let 0 le theta le pi/2 and x=X cos theta...

Let `0 le theta le pi/2` and `x=X cos theta + Y sin theta, y=X sin theta Y cos theta ` such that `x^(2)+2xy+y^(2)=aX^(2)=bY^(2)`, where a and b are constant then

A

`a=-1,b=3,theta=(pi)/(4)`

B

`a=1,b=-3,theta=(pi)/(3)`

C

`a=3,b=-1,theta=(pi)/(4)`

D

`a=3,b=-1,theta=(pi)/(3)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-CARTESIAN CO-ORDINATE SYSTEM -Exercise
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  4. If the coordinates of orthocentre O' are centroid G of a DeltaABC are ...

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  6. If C and D are the points of internal and external division of line se...

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  7. If the centroid of a triangle is (1,\ 4) and two of its vertices...

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  8. A triangle with vertices (4, 0), (-1,-1), (3,5), is

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  9. The angle through which the coordinates axes be rotated so that xy-ter...

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  10. In order to make the first degree terms missing in the equation 2x^2+7...

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  11. When the origin is shifted to a suitable point, the equation 2x^2+y^2-...

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  12. If by shifting the origin at (1,1) the coordinates of a point P become...

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  13. By rotating the coordinates axes through 30^(@) in anticlockwise sens...

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  14. In Delta ABC, the sides BC =5,CA=4 and AB=3. If A-=(0,0) and the inter...

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  15. The harmonic conjugate of (4,-2) with respect to (2,-4) and (7,1) is

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  16. If the coordinates of the centroid and a vertex oc an equilaterqal tri...

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  17. The transformed equation of 3x^(2)+3y^(2)+2xy-2=0 when the coordinats ...

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  18. The transformed equation of x^(2)+6xy+8y^(2)=10 when the axes are rota...

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  19. Let 0 le theta le pi/2 and x=X cos theta + Y sin theta, y=X sin theta ...

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  20. If X=x cos theta-y sin theta, Y=x sin theta+y cos theta and X^(2)+4XY...

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