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If l and m are variable real number such...

If l and m are variable real number such that `5l^(2)+6m^(2)-4lm+3l=0`, then the variable line lx+my=1 always touches a fixed parabola, whose axes is parallel to the x-axis.
The focus of the parabola is

A

`(1/6,-7/6)`

B

`(1/3,4/3)`

C

`(3/2,-3/2)`

D

`(-3/4,3/4)`

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The correct Answer is:
B
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FIITJEE-PARABOLA-SOLVED PROBLEMS (OBJECTIVE )
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  2. The co-ordinates of the points on the barabola y^(2) =8x, which is at ...

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  3. AB is a focal chord of y^(2)=4x with A(2,2sqrt2). The radius of the ci...

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  4. Let S be the set of all possible values of parameter 'a' for which the...

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  5. If a normal chord at a point on the parabola y^(2)=4ax subtends a righ...

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  6. Find the equation of the straight lines touching both x^2+y^2=2a^2 and...

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  7. The equation 2y^(2)+3y-4x-3=0 represents a parabola for which

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  8. Consider the circle x^2+y^2=9 and the parabola y^2=8x. They intersect ...

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  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  10. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  11. If l and m are variable real number such that 5l^(2)+6m^(2)-4lm+3l=0, ...

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  12. If l and m are variable real number such that 5l^(2)+6m^(2)-4lm+3l=0, ...

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  13. Statement-1: The maximum value of |sqrt(x^(4)-3x^(2)-6x+13)-sqrt(x^(4)...

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  14. Normal at the point A(2, -4) intersect the parabola y^(2)=8x at the po...

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  15. Normals are drawn from the interior point P to the parabola y^(2)=4x s...

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  16. Match the following:

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  17. If normals to parabola y^(2)=4x at points A, B, C intersect at (11, 0)...

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  18. Column I : Parabola y^(2)=16x is given. In column I, 4 points (P) is g...

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  19. Column I : Parabola y^(2)=16x is given. In column I, 4 points (P) is g...

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  20. Column I : Parabola y^(2)=16x is given. In column I, 4 points (P) is g...

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