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If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

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The correct Answer is:
`x^(2)+8y=32`
Focus is (0,2) and vertex is (0,4).
so, axis of the parabola is y-axis.
Also, parabola is concave downward.
Distance between focus and directrix is a=2.
`:.` Latus rectum = 4a=8
So, using equation `(x-h)^(2)=4a(y-k)`, equation of parabola is `(x-0)^(2)=-8(y-4)`
`or" "x^(2)+8y=32`
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CENGAGE PUBLICATION-PARABOLA-Concept Applications 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. Check wheather Rolle's theorem is applicable on f(x) = x^2-8x+12 on [...

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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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