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If `alpha and beta` are two points on the hyperbola `x^(2)/a^(2)-y^(2)/b^(2)=1` and the chord joining these two points passes through the focus (ae, 0) then `e cos ""(alpha-beta)/(2)=`

A

` cos ""( alpha +beta )/(2) `

B

` cos""(alpha -beta )/( 2) `

C

` cos ""( 2alpha-2 beta )/( 4) `

D

` sin ""( alpha +beta )/( 2) `

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-Hyperbola -EXERCISE 1A
  1. A normal to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 cuts the axes...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Chords of an elipse are drawn through the positive end of minor axis ....

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  20. The locus of the point represented by x = 1 + 4 cos theta , ...

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