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Find the length of the latus rectum of t...

Find the length of the latus rectum of the parabola whose focus is at (2, 3) and directrix is the line `x-4y+3=0` .

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Verified by Experts

The correct Answer is:
`(14)/(sqrt(17))`
Perpendicular distance of the focus from the directrix
`2a=|-(7)/(sqrt(17))|=(7)/(sqrt(17))`
`:." Length of latus rectum"=4a=(14)/(sqrt(17))`
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CENGAGE-PARABOLA-Exercise 5.2
  1. If the focus and vertex of a parabola are the points (0, 2) and (0, 4)...

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  2. Find the equation of parabola whose focus is (0,1) and the directrix i...

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  3. Find the vertex, focus and directrix of the parabola x^(2)=2(2x+y).

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  4. The vertex of a parabola is (2, 2) and the coordinats of its two ex...

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  5. A parabola passes through the point the point (1,2), (2,1), (3,4) and ...

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  6. Find the length of the common chord of the parabola x^2=4(x+3) and the...

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  7. The equation of the latus rectum of a parabola is x+y=8 and the equati...

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  8. Find the length of the latus rectum of the parabola whose focus is at ...

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  9. If (a ,b) is the midpoint of a chord passing through the vertex of the...

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  10. Show that the locus of a point that divides a chord of slope 2 of the ...

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  11. Plot the region in the first quadrant in which points are nearer to th...

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  12. Prove that the locus of a point, which moves so that its distance from...

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  13. Prove that the locus of the center of a circle, which intercepts a cho...

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  14. Find the equation of the parabola whose focus is S(-1,1) and directrix...

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  15. The axis of parabola is along the line y=x and the distance of its ver...

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  16. Find the equation of parabola whose focus is (0,1) and the directrix i...

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  17. Find the vertex, focus and directrix of the parabola x^(2)=2(2x+y).

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