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The vertex of a parabola is (2, 2) and t...

The vertex of a parabola is (2, 2) and the coordinats of its two extremities of latus rectum are `(-2,0)` and (6, 0). Then find the equation of the parabola.

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The correct Answer is:
`(x-2)^(2)=-8(y-2)`
Focus is midpoint of the extremities of latus rectum.
Thus, focus is (2,0).
Distance between focus and vertex is a=2.
Also, axis of the parabola is x=2 and parabola is concave downward as focus lies below the vertex.
Therefore, using equation `(x-h)^(2)=-4a(y-k)`, required equation of parabola is
`(x-2)^(2)=-8(y-2)`
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CENGAGE-PARABOLA-Exercise 5.2
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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. about to only mathematics

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

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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 a parabola is along the line y=x and the distance of its v...

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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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