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Prove that the straight lines joining the origin to the points of intersection of the straight line `hx+ky=2hk` and the curve `(x-k)^(2)+(y-h)^(2)=c^(2)` are at right angle if `h^(2)+k^(2)=c^(2)`.

A

`h^2+k^2+c^2=0`

B

`h^2-k^2-c^2=0`

C

`h^2+k^2-c^2=0`

D

none of these

Text Solution

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The correct Answer is:
C
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FIITJEE-STRAIGHT LINE -SOLVED PROBLEMS (OBJECTIVE)
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  2. If the straight lines ax+by+c=0 and xcosalpha+ysinalpha=c encloses an ...

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  3. Prove that the straight lines joining the origin to the points of inte...

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  4. The value of k for which the equation 2x^2+5y^2-2ky+4x+6y=0 represent ...

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  5. Triangle ABC lies in the Cartesian plane and has an area of 70 sq. uni...

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  6. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

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  7. The equation of smaller circle of radius sqrt3-1 in l^(st) quadrant ha...

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  8. The coordinates of the points (s) on the line x + y = 5 , which is/ ar...

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  9. ABCD is a square Points E(4,3) and F(2,5) lie on AB and CD, respective...

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  10. ABCD is a rectangle with A(-1,2) , B (3,7) and AB : BC = 4 : 3 . If d ...

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  11. If (x/a)+(y/b)=1 and (x/c)+(y/d)=1 intersect the axes at four concylic...

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  12. Two consecutive sides of a parallelogram are 4x+5y=0a d n7x+2y=0. If t...

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  13. Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0...

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  14. Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0...

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  15. The line 6x + 8y - 48 intersects the co - ordinate axis at A and B res...

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  16. The line 6x + 8y - 48 intersects the co - ordinate axis at A and B res...

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  17. Statement -1 : The lines ai x + bi y + c i=0,i={1,2,3} are concurrent ...

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  18. Statement -1 : The minimum value of (x2-x1)^2+(sqrt(1+x1^2)-sqrt(4-x2^...

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  19. Given four parallel lines L1,L2,L3 and L4 Let the distacnes between th...

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