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A quadrilateral is inscribed in a parabo...

A quadrilateral is inscribed in a parabola . Then,

A

the quadrilateral may be cyclic

B

diagonals of the quadrilateral may be equal

C

all possible pairs of adjacent sides may be perpendicular

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B
1,2
As a circle can intersect a parabola at four points, the quadrilateral may be cyclic.
The diagonals of the quadrilateral may be equal as the quadrilateral may be an isosceles trapezium.
A rectangle cannot be inscribed in a parabola. So, option (3) is wrong.
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CENGAGE-PARABOLA-Exercise (Multiple)
  1. The value(s) of a for which two curves y=ax^(2)+ax+(1)/(24)andx=ay^(2)...

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  2. In which of the following cases, a unique parabola will be obtained ?

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  3. A quadrilateral is inscribed in a parabola . Then,

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  4. The locus of the midpoint of the focal distance of a variable point ...

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  5. A square has one vertex at the vertex of the parabola y^2=4a x and the...

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  6. If two distinct chords of a parabola y^2=4ax , passing through (a,2a) ...

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  7. Let PQ be a chord of the parabola y^2=4x. A circle drawn with PQ as a...

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  8. If the parabola x^2=ay makes an intercept of length sqrt40 unit on the...

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  9. The equation of the directrix of the parabola with vertex at the origi...

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  10. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

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  11. The parabola y^2=4x and the circle having its center at 6, 5) intersec...

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  12. Which of the following line can be tangent to the parabola y^2=8x ? x...

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  13. If the line k^(2)(x-1)+k(y-2)+1=0 touches the parabola y^(2)-4x-4y+8=0...

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  14. The equation of the line that touches the curves y=x|x| and x^2+(y^2-2...

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  15. The equations of the common tangents to the parabola y = x^2 and y=-...

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  16. The line x+ y +2=0 is a tangent to a parabola at point A, intersect t...

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  17. Which of the following line can be normal to parabola y^2=12 x ? x+y-...

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  18. A normal drawn to the parabola =4a x meets the curve again at Q such t...

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  19. A circle is drawn having centre at C (0,2) and passing through focus ...

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  20. From any point P on the parabola y^(2)=4ax, perpebdicular PN is drawn ...

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