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A variable straight line is drawn throug...

A variable straight line is drawn through the point of intersection of the straight lines `x/a+y/b=1` and `x/b+y/a=1` and meets the coordinate axes at `A` and `Bdot` Show that the locus of the midpoint of `A B` is the curve `2x y(a+b)=a b(x+y)`

A

`alpha beta ( x + y) = xy (alpha + beta)`

B

`alpha beta ( x + y) = 2xy (alpha + beta)`

C

`(alpha + beta) ( x + y) = 2 alpha beta xy`

D

none of these

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B
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OBJECTIVE RD SHARMA ENGLISH-STRAIGHT LINES-Exercise
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  2. If a variable line passes through the point of intersection of the lin...

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  3. A variable straight line is drawn through the point of intersection of...

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  4. The nearest point on the line 3x- 4y = 25 from the origin is

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  5. The distance between the lines (x+7y)^2+4sqrt(2)(x+7y)-42=0 is

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  6. The image of the point (-1,3) by the line x - y = 0 , is

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  7. If A(1,1), B(sqrt3+1,2) and C(sqrt3,sqrt3+2) are three vertices of a s...

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  8. If (-4,0) and (1,-1) are two vertices of a triangle of area 4s qdotu n...

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  9. If the line x+y-1=(lamda)/(2)=0 passing through the intersection of ...

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  10. The distance between the lines 5x+12y+65=0 and 5x+12y-39 = 0 is :

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  11. Prove that the locus of the centroid of the triangle whose vertices ar...

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  12. The equation of the line with slope -3//2 and which in concurrent with...

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  13. The point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 lies on

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  14. Find the equation of the bisector of the obtuse angle between the line...

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  15. If the equation of the locus of a point equidistant from the points (a...

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  16. The equations of perpendicular bisectors o the sides AB and AC of a ...

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  17. If each of the points (x1,4),(-2,y1) lies on the line joining the poin...

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  18. Equation of the line passing through the point (acos^3theta, a sin^3th...

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  19. The ends of the base of an isosceles triangle are at (2a, 0)and (0, a)...

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  20. The straight line x+y-4=0,3x+y-4=0,x+3y-4=0 form a triangle which is

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