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If l and m are variable real numbers suc...

If `l` and` m` are variable real numbers such that `5l^2-4lm+6m^2+3l=0`, then the variable line `lx+my=1` always touches a fixed parabola, whose axis is parallel to the X-axis.
If ex+f=0 is directrix of the parabola and e,f are prime numbers , then the value of `|e-f|` is

A

2

B

4

C

6

D

8

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The correct Answer is:
D
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ARIHANT MATHS-PARABOLA-Exercise (Passage Based Questions)
  1. Let C be the locus of the circumcentre of a variable traingle having s...

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  2. Find dy/dx if y^2=4lamdax

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  3. The locus of the circumcenter of a variable triangle having sides the ...

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  4. The focus of the parabola x^2-8x+2y+7=0 is

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  5. The focus of the parabola x^2-8x+2y+7=0 is

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  6. Consider a parabola x^2-4xy+4y^2-32x+4y+16=0. The focus of the parab...

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  7. If l and m are variable real numbers such that 5l^2-4lm+6m^2+3l=0, the...

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  8. If l and m are variable real numbers such that 5l^2-4lm+6m^2+3l=0, the...

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  9. Find the slope of tangent to the curve if equation of the curve is y^2...

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  10. Find the slope of normal to the curve if equation of the curve is y^2=...

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  11. Find dy/dx if y^2=10x

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  12. Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of t...

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  13. Tangent to the parabola y=x^2+ax+1 at the point of intersection of the...

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  14. Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of t...

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  15. Find the slope of tangent to the curve if equation of the curve is x^2...

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  16. A parabola (P) touches the conic x^2+xy+y^2-2x-2y+1=0 at the points w...

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  17. A parabola (P) touches the conic x^2+xy+y^2-2x-2y+1=0 at the points w...

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  18. y=3x is tangent to the parabola 2y=ax^2+b. The minimum value of a+b i...

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  19. y=3x is tangent to the parabola 2y=ax^2+b. If (2,6) is the point of ...

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  20. y=3x is tangent to the parabola 2y=ax^2+ab. If b=36,then the point o...

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