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The line lx+my+n=0 intersects the curve ...

The line `lx+my+n=0` intersects the curve `ax^2 + 2hxy + by^2 = 1` at the point P and Q. The circle on PQ as diameter passes through the origin. Then `n^2(a+ b)` equals (A) `l^2+m^2` (B) `2lm` (C) `l^2-m^2` (D) `4lm`

A

`n^(2)(a+b)`

B

`n^(2)(a+b)^(2)`

C

`n^(2)(a^(2)-b^(2))`

D

`n^(2)(a^(2)+b^(2))`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-CIRCLES-Chapter Test
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  2. Show that the four points of intersection of the lines : (2x-y + 1) (x...

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  3. If 2x+3y-6=0 and 9x+6y-18=0 cuts the axes in concyclic points, then th...

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  4. The line lx+my+n=0 intersects the curve ax^2 + 2hxy + by^2 = 1 at the ...

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  5. Two circles, each of radius 5, have a common tangent at (1, 1) whose e...

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  6. PQ is a chord of the circle x^(2)+y^(2)-2x-8=0 whose mid-point is (2, ...

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  7. The number of circles belonging to the system of circles 2(x^(2)+y^(2)...

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  8. The equation of the circle passing through (0, 0) and belonging to the...

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  9. If (-1/3,-1) is a centre of similitude for the circles x^2+y^2=1 and x...

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  10. If P(1, 1//2) is a centre of similitude for the circles x^(2)+y^(2)+4...

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  11. Statement 1 : The equation x^2+y^2-2x-2a y-8=0 represents, for differe...

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  12. x=1 is the radical axis of the two orthogonally intersecting circles....

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  13. If the y=mx+1, of the circle x^2+y^2=1 subtends an angle of measure 45...

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  14. The circles x^2 + y^2 + 6x + 6y = 0 and x^2 + y^2 - 12x - 12y = 0

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  15. The equation of the pair of straight lines parallel to x-axis and touc...

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  16. The equation of the circumcircle of the triangle formed by the lines x...

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  17. The value of lambda for which the circle x^(2)+y^(2)+2lambdax+6y+1=0 i...

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  18. The equation of the circle concentric to the circle 2x^(2)+2y^(2)-3x+6...

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  19. If the angle of intersection of the circle x^2+y^2+x+y=0 and x^2+y^2+x...

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  20. The equation of the image of the circle (x-3)^(2)+(y-2)=1 in the mirro...

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