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Consider the parabola y^2 = 8x. Let Delt...

Consider the parabola `y^2 = 8x.` Let `Delta_1` be the area of the triangle formed by the end points of its latus rectum and the point P(`1/2`,2) on the parabola and `Delta_2` be the area of the triangle formed by drawing tangents at P and at the end points of latus rectum. `Delta_1/Delta_2` is :

Text Solution

Verified by Experts

The correct Answer is:
2
As, we have area of` Delta` formed by three points on parabola is twice the arae of `Delta` formed by corresponding tangents i.e., of `Delta PQR = 2` area of
`Delta T_(1) T_(2) T_(3)`.
`:. Delta_(1) = 2 Delta_(2)` or `(Delta_(1))/(Delta_(2)) = 2`
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Knowledge Check

  • The end points of the latus rectum of the parabola x ^(2) + 5y =0 is

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    `(pm (5)/(2), -(5)/(4))`
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    `(pm (2)/(5), pm (4)/(5))`
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    `(pm (4)/(5), pm (4)/(5))`
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