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A normal to the hyperbola x^(2)//a^(2) ...

A normal to the hyperbola ` x^(2)//a^(2) -y^(2)//b^(2) =1` cuts the axes at K and L. The perpendicular at K and L to axes meet in P. The locus of P is

A

` a^(2)x^(2) +b^(2) y^(2) =(a^(2)+b^(2) )^(2) `

B

` a^(2)x^(2) -b^(2)y^(2) =(a^(2) +b^(2))^(2) `

C

` a^(2) x^(2) +b^(2)y^(2) =(a^(2) -b^(2) )^(2) `

D

` a^(2) x^(2) -b^(2) y^(2) =(a^(2) -b^(2))^(2) `

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-Hyperbola -EXERCISE 1A
  1. Let A (2sec theta, 3 tan theta ) and B( 2sec phi ,3 tan phi ) where t...

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  2. P(theta ) and Q( phi ) are two point on x^(2)//a^(2) -y^(2)//b^(2) =...

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  3. A normal to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 cuts the axes...

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  4. If the normal at theta on the hyperbola x^(2)//a^(2) -y^(2) //b^(2)...

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  5. If alpha and beta are two points on the hyperbola x^(2)/a^(2)-y^(2)/b^...

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  6. If the axes are rotated through an angle of 45^(@) in the anticlockw...

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  7. If the circle x ^(2) +y^(2) =a^(2) intersects the hyperbola xy =c^(...

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  8. If PN is the perpendicular from a point on a rectangular hyperbola to ...

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  9. The conic represented by x^(2) -4x+ 3y -1=0 is

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  10. The conic represented by 2x^(2) -12xy +23y^(2) -4x -28y -48 =0 is

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  11. x^(2) -y^(2) +5x +8y -4=0 represents

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  12. The equation 16x^(2)+y^(2) +8xy-74x-78y+212 =0 represents

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  13. The equation (x^(2))/(12-k) +(y^(2))/( 8-k) =1 represents

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  14. A point moves in a plane so that its distances PA and PB from the two ...

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  15. The curve represented by x=3 (cos t + sin t ) ,y =4 (cos t -sin t ) ...

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  16. The curve represented by x=2 (cos t +sin t ) , y=5 (cos t -sin t ) is

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  17. The curve represented by x= a( cos h theta + sin h theta) , y =b ( co...

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  18. The graph represented by the equations x= sin ^(2) t, y = 2 cos t is

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  19. If m is a variable the locus of the point of intersection of the lines...

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  20. The curve describe parametrically by x =t^(2) +t+1,y=t^(2) -t+1 repre...

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